Options UG

8/10/2019 Options UG

1/234

CQG IntegratedClient Options UserGuideFebruary 22, 2013 | Version 14.1


2/234

2013 CQG Inc.

CQG, DOMTrader, SnapTrader, TFlow, and TFOBV are registered trademarks of CQG.


3/234

Table of Contents

About this Document .................................................................................................. 1

Whats New in this Version ....................................................................................... 2

Related Documents .................................................................................................. 2

Customer Support ................................................................................................... 2

Options in CQG .......................................................................................................... 3

Entering Options Symbols ......................................................................................... 4

Opening Options Applications .................................................................................... 5

CQG API and Options ............................................................................................... 6

Greeks and Volatility Definitions ................................................................................ 7

Standard Options Pricing Models ............................................................................... 9

Exotic Option Models.............................................................................................. 23

Interest-Rate Option Models ................................................................................... 32

Spread Options Model ............................................................................................ 41

Cumulative Normal Distribution Function Approximation ............................................. 46

Numerical Methods for Solving Equations ................................................................. 47

Numerical Differentiation ........................................................................................ 48

Trading Options..................................................................................................... 49

Setting Options Preferences ....................................................................................... 51

Setting Options Window View Preferences ................................................................ 53

Setting Options Calculator View Preferences ............................................................. 54

Setting Volatility Workshop View Preferences ............................................................ 55

Setting Strategy Analysis View Preferences............................................................... 57

Setting Volatility Preferences .................................................................................. 58

Setting Interest Rate Preferences ............................................................................ 60

Setting Price Filter Preferences ................................................................................ 61

Setting Greeks Scale Preferences ............................................................................ 62

Setting Advanced Preferences ................................................................................. 63

Setting Model Preferences ...................................................................................... 64

Setting Update Frequency Preferences ..................................................................... 65

Updating the Refresh Rate ...................................................................................... 66

Options Window ....................................................................................................... 67

Options Window Toolbar ......................................................................................... 72

Customizing Columns ............................................................................................. 75


4/234

Changing the Order of Columns ............................................................................... 78

Marking At-the-Money ............................................................................................ 79

Changing the Display Type ..................................................................................... 80

Opening Another Application from an Options Window ............................................... 81

Setting What If Options Parameters ......................................................................... 82

Copying Data to Excel ............................................................................................ 83

Placing Orders from the Options Window .................................................................. 84

Options Calculator .................................................................................................... 85

Options Calculator Components ............................................................................... 86

Options Calculator Toolbar ...................................................................................... 88

Using the Options Calculator ................................................................................... 90

Inputting What Ifs ................................................................................................. 92

Viewing Summary Statistics .................................................................................... 93

Using the Options Calculator Graph ......................................................................... 94

Using Cursors with an Options Calculator Graph ...................................................... 101

Information Displayed in an FX OTC View ............................................................... 102

Selecting the Properties for the Options Calculator Graph Lines ................................. 106

Options Graph ....................................................................................................... 107

Options Graph Toolbar ......................................................................................... 108

Define Options Graph Curves ................................................................................ 113

Volatility Workshop................................................................................................. 125

Volatility Workshop Components ........................................................................... 126

Volatility Workshop Toolbar .................................................................................. 129

Saving the Volatility Curve ................................................................................... 136

Opening a Saved Volatility Curve ........................................................................... 137

Adjusting the shape of the curve ........................................................................... 139

Removing Corrections .......................................................................................... 140

Selecting the Colors for the Volatility Workshop Graph Lines ..................................... 141

Designating the Approximation Characteristics ........................................................ 142

Modifying the Volatility Curve ................................................................................ 147

Resetting the Volatilities ....................................................................................... 148

Using 3D ............................................................................................................ 149

Strategy Analysis Window ....................................................................................... 153

Strategy Analysis Window Components .................................................................. 154

Strategy Analysis Toolbar ..................................................................................... 159

Selecting a Strategy ............................................................................................ 161


5/234

Selecting an Underlying Model for Strategy Displays ................................................ 164

Table Tabs .......................................................................................................... 171

Using the Display Tabs ......................................................................................... 187

Setting Properties for 3D Strategy Graph ................................................................ 191

Underlying Information ........................................................................................ 198

Display Properties................................................................................................ 199

Creating and Editing Strategies ............................................................................. 208

Saving an Options Strategy .................................................................................. 212

Loading a Saved Strategy ..................................................................................... 214

Using the Strategy Workspace Manager Window ..................................................... 215

Weights.............................................................................................................. 216

Using Advanced Strategy Features......................................................................... 221

Options Strategy Color Windows ........................................................................... 226


6/234


7/234

Page 1

Options User Guide

About this Document

This document is one of several user guides for CQG Integrated Client (CQG IC). This guidedetails options-specific tools in CQG.

You can navigate the document in several ways:

Click a bookmark listed on the left of the page.

Click an item in the Table of Contents.

Click a blue, underlined link that takes you to another section of the document. To goback, use Adobe Reader Page Navigation items (Viewmenu).

If you are looking for a particular term, it may be easier for you to search the document for it.

There are two ways to do that:

Right-click the page, and then click Find.

Press Ctrl+F on your keyboard.

This document is intended to be printed double-sided, so it includes blank pages before new

chapters.

Please note that images are examples only and are meant to demonstrate and expose system

behavior. They do not represent actual situations.

To ensure that you have the most recent copy of this guide, pleasego to the user guide page

on CQGs website.
http://www.cqg.com/Support/User-Guide.aspxhttp://www.cqg.com/Support/User-Guide.aspxhttp://www.cqg.com/Support/User-Guide.aspxhttp://www.cqg.com/Support/User-Guide.aspxhttp://www.cqg.com/Support/User-Guide.aspxhttp://www.cqg.com/Support/User-Guide.aspx


8/234

Page 2

About this Document

Whats New in this Version

Weve added a Costbutton and a multiplier button to theOptions Window toolbar.

Related Documents

CQG IC user guides:

CQG Basics

Charting and Studies

Advanced Analytics

TradingandCQG Spreader

Customer SupportCQG Customer Support can be reached by phone from Sunday, 2:30 p.m. CT through Friday,

5:00 p.m. CT. These hours also apply to Live Chat.

United States 1-800-525-1085

United Kingdom +44 (0) 20-7827-8270

France +33 (0) 1-74-18-07-81

Germany +49 (0) 69-6677-7558-0

Japan +81 (0) 3-3286-6877

Russia +7 495-795-2409

Singapore +65 6494-4911

Sydney +61 (2) 9235-2009

[email protected] hours a day, 7 days a week.

If you have questions about CQG documentation, pleasecontact the help author.
http://www.cqg.com/Docs/CQG_Basics_UG.pdfhttp://www.cqg.com/Docs/CQG_Basics_UG.pdfhttp://www.cqg.com/Docs/Charting_UG.pdfhttp://www.cqg.com/Docs/Charting_UG.pdfhttp://www.cqg.com/Docs/Analytics_UG.pdfhttp://www.cqg.com/Docs/Analytics_UG.pdfhttp://www.cqg.com/Docs/Trading_UG.pdfhttp://www.cqg.com/Docs/Trading_UG.pdfhttp://www.cqg.com/Docs/CQGSpreaderUserGuideTrader.pdfhttp://www.cqg.com/Docs/CQGSpreaderUserGuideTrader.pdfhttp://www.cqg.com/Docs/CQGSpreaderUserGuideTrader.pdfmailto:[email protected]:[email protected]:[email protected]:[email protected]?subject=DeMark%20User%20Guidemailto:[email protected]?subject=DeMark%20User%20Guidemailto:[email protected]?subject=DeMark%20User%20Guidemailto:[email protected]?subject=DeMark%20User%20Guidemailto:[email protected]://www.cqg.com/Docs/CQGSpreaderUserGuideTrader.pdfhttp://www.cqg.com/Docs/Trading_UG.pdfhttp://www.cqg.com/Docs/Analytics_UG.pdfhttp://www.cqg.com/Docs/Charting_UG.pdfhttp://www.cqg.com/Docs/CQG_Basics_UG.pdf


9/234

Page 3

Options User Guide

Options in CQG

CQG IC includes five options applications:

Options Window

Options Calculator

Options Graph

Volatility Workshop

Strategy Analysis

All CQG IC users have access to the Options Window and the Options Graph. If you would liketo learn more about our advanced options offering, which includes Options Calculator, Options

Strategy, and Volatility Workshop,please contact CQG.

CQG offers seven basic option models that serve as the framework for valuing options: Black,

Black-Scholes, Bourtov, Cox-Ross-Rubinstein, Garman-Kohlhagen, Merton, and Whaley.
http://www.cqg.com/Support.aspxhttp://www.cqg.com/Support.aspxhttp://www.cqg.com/Support.aspxhttp://www.cqg.com/Support.aspx


10/234

Page 4

Options in CQG

Entering Options Symbols

The format for options on futures is: C. for calls

and or P. for puts.

The strike price is 2-5 digits.

Example: C.SPZ081500 = December 2008 1500 call on the S&P 500 futures contract.

An alternate format is C._. for calls and with P.for puts.

C.SP_U8.1500 = September 2008 1500 call on the S&P 500 futures contract.

On Options windows, you can enter the symbol only.

For at the money for the nearby month, type C. or P., the symbol, and ?.

For at the money for some other month, type C.orP., the symbol, the month, the year, and ?

and then press CTRL+ENTER.

For strikes for the most active month, type C.or P.and the symbol and ?and then pressCTRL+ENTER.


11/234

Page 5

Options User Guide

Opening Options Applications

Click the Optionsbutton on the main toolbar, and then click the name of the options window

you want to open:

This button provides access to all options windows without having to display the button for each

window.

If the Optionsbutton is not displayed, click the Morebutton, and then click Options.

You can also add individual options windows to the toolbar:


12/234

Page 6

Options in CQG

CQG API and Options

CQGs API supports efficient access to options strike properties through the use of the

CQGInstrumentsGroup interface.

With one request to CQG servers, your application can subscribe to all strikes in any givencontract month or a range of months.

Data subscription levels can also be configured to optimize instrument resolution for strikeproperties and market data, allowing for the delivery of critical information without unnecessary

overhead.

CQG also offers access to common real-time values for all subscribed options strikes: Greeks,

theoretical values and implied volatilities.

Through the API, CQG offers in-depth portfolio analysis capabilities.


13/234

Page 7

Options User Guide

Greeks and Volatility Definitions

As you work with options in CQG IC, its helpful to understand how implied and average

volatility are calculated and how the Greeks are defined.

Delta

Delta shows the change in the price of a derivative to the change in the price of the underlyingassets. Sometimes delta is known as the hedge ratio, as delta indicates how much of theunderlying asset needs to be bought or sold to hedge the option. Traders take advantage of

delta by creating delta hedging, delta spreads, and delta neutral.

Delta values are positive numbers less than or equal to 100. They represent the ratio of thechange in the theoretical value over the change in the underlying price.

Values:

Out of the money = close to 0

At the money = close to +0.5

In the money = close to +1

Calls = positive

Puts = negative

Delta values for the out-of-the-money series move closer to 0 as expiration nears. Likewise,

more in-the-money options have deltas close to 1 as expiration approaches.

For example: If the underlying S&P 500 contract stands at 134020, with a delta of 52.73, and a

theoretical value of 2600.5, and the underlying price increases to 134220, while the delta risesto 54.02, the theoretical value increases to 2707.

The calculations are:

134220 134020 = 200

(52.73 + 54.02)/2 = 106.750

53.375 *2 = 106.750

The deltas from one underlying price to the next are interpolated.

106.750 + 2600.5 = 2707.25 new theoretical value

Gamma

Gamma is the amount the delta changes when the underlying price changes by one tick.

Gamma is greatest for at-the-money options. Gamma increases as the option moves closer to

expiration. Traders try to limit gamma risk because short gamma positions create a potentialfor losses.

For example: If the delta of an S&P future was 91.80, the gamma was .01 and the price of an

S&P future increased from 1340.80 to 1340.90 i.e., a one-tick increase, the delta wouldincrease to 91.81.


14/234

Page 8

Options in CQG

Theta

Theta represents the loss in theoretical value in one day, if all other factors are constant. Inother words, it attempts to isolate the time decay factor.

For example: Assume the amount showing the Value column was 2725.1, with 15 days until

expiration and a theta value of 92.053. You would expect to see the amount in the Valuecolumn decrease approximately 92 dollars the following day. A more precise definition of the

amount of the time value lost is an average of the Thetas on the dates under consideration. So,if the theta on the following day was 95.201, the decrease in theoretical value would be:

(92.053 + 95.201)/2 = 93.6

Vega

Vega is the amount that the theoretical value changes when the volatility changes by 1 point.

For example: Assume a June Corn contract had a vega of 1.421, a volatility of 25.90, and atheoretical value of 45.4. If the volatility were to increase to 26.90, the vega says that the

theoretical value would increase by 1.4 dollars to 46.8, provided the other factors affectingoptions prices remained constant.

The display also indicates the days until expiration, as well as the volatility and interest rate

assumptions underlying the data.

Rho

Rho is the change in option price to a unit change in interest rates. When the interest rateincreases, the call option price increases also and put option price falls.

For example: Assume the starting call value is 4.2012, the interest rate r is 5% and zero-coupon rate b is 2%. Rho(r)(per 1%)= 0.1243, and Rho(b)(per 1%)=0.1328, If r rises to 6%

and b stays at 5%, the call value is 4.3255. If r stays at 5% and b rises to 3%, the call value is4.334.

Implied Volatility

The implied volatility calculated from an options display represents the volatility that, if entered

into a theoretical pricing model, would produce a theoretical value equal to the market price of

the option. Unlike the Historical Volatility study, the Implied Volatility calculation depends onthe model selected, the calculation method chosen and the parameters input in the What if?

column.

Average Volatility

The average volatility is calculated using the following formula:

( ) ( )( )LH

LHHL

SPSP

SPUPIVUPSPIVAvgV

+=


15/234

Page 9

Options User Guide

Standard Options Pricing Models

Options pricing models describe mathematically how a set of input parameters typically

underlying price, strike price, time to expiration, interest rate, and volatility combine to

determine a theoretical value of an option.CQG offers seven basic option models that serve as the framework for valuing options: Black,

Black-Scholes, Bourtov, Cox-Ross-Rubinstein, Garman-Kohlhagen, Merton, and Whaley.

Term Definition

TheoV option theoretic value

sigma, volatility of the relative price change of the underlying stock price

ImpV implied volatility

Greeks Partial derivatives of the option price to a small movement in the underlying

variables. Main greeks are delta, gamma, theta, vega, rho.

Delta, delta is the first derivative of the option price by underlying price

Gamma, gamma is the second derivative of the option price by underlying price

Vega vega is the first derivative of the option price by volatility

Theta, theta is the first derivative of the option price by time to expiration

Rho, rho is the first derivative of the option price by interest rate

N(x) the cumulative normal distribution function

n(x) normal distribution function

,

S underlying price

X strike price of option

r risk-free interest rate

T option time to expiration in years

=

x z

dzexN 22

2

1)(

2

2

2

1)(

x

exn

=

2

2

2

1)(

x

exxn

=


16/234

Page 10

Options in CQG

Term Definition

volatility of the relative price change of the underlying instrument

b the cost-of-carry rate of holding the underlying security

For further reading, we suggest:

The Complete Guide to Option Pricing Formulas. ISBN 0071389970.

Options, Futures, and Other Derivatives. ISBN 0132164949.

Option Volatility and Pricing Strategies. ISBN155738486X.


17/234

Page 11

Options User Guide

Black Model

In 1976, Fisher Black developed a modification to the Black-Scholes model designed to price

options on futures more precisely. The model assumes that futures can be treated the sameway as securities, providing a continuous dividend yield equal to the risk-free interest rate.

The model provides a good correction to the original model concerning options on futures.

However, it still carries the restrictions of the Black-Scholes evaluation.

Notation

Theoretical value of a call

Theoretical value of a put

Underlying price

Strike price

Interest rate

Time to expiration in years

Volatility

Cumulative normal density function

The theoretical values for calls and puts are:

Where:

Note: Although similar, this definition of is different from the one used in the Black-Scholesmodel.

An alternative form for is:

C

P

U

E

r

t

)(xN

)()( thNEehNUeC rtrt =

)()( htNEehNUeP rtrt +=

2

)/ln( t

t

EUh

+=

h

h

t

tEUh

2

)/ln(2 2+=


18/234

Page 12

Options in CQG

Generalized Black-Scholes (Black-Scholes extended) Model

The generalized Black-Scholes model can be used to price European options on stocks without

dividends [Black and Scholes (1973) model], stocks paying a continuous dividend yield [Merton(1973) model], options on futures [Black (1976) model], and currency options [Garman and

Kohlhagen (1983) model].

TheoV

Call

Put

where

N(x) the cumulative normal distribution function;

S underlying price;

X strike price of option;

r risk-free interest rate;

T time to expiration in years;

volatility of the relative price change of the underlying stock price.

b the cost-of-carry rate of holding the underlying security.

b = r gives the Black and Scholes (1973) stock option model.

b = r q gives the Merton (1973) stock option model with continuous dividend yield q.

b = 0 gives the Black (1976) futures option model.

b = r rf gives the Garman and Kohlhangen (1983) currency option model (rf- risk-free

rate of the foreign currency).

Delta

Call

Put

)()(C 21)(

GBS dNeXdNeSc TrTrb ==

)()(P 1)(

2GBS dNeSdNeXp TrbTr ==

( )T

TbXSd

++=

2/)/ln( 2

1

Tdd = 12

)( 1)(

dNe Trb=

[ ]1)( 1)( = dNe Trb


19/234

Page 13

Options User Guide

Gamma

Gamma is identical for put and call options.

where

- normal distribution function.

Vega

Vega is identical for put and call options.

Theta

Call

Put

Rho

Call

where

c call TheoV

Put

where

p put TheoV

TS

edn Trb

=

)(

1)(

2

2

2

1)(

x

exn

=

TdneSVega Trb = )( 1

)(

)()()(2

)(21

)(1

)(

dNXrdNeSrbT

dneS rTTrbTrb

++

=

)()()(2

)(21

)(1

)(

dNXrdNeSrbT

dneS rTTrbTrb

=

=

=

0

0),( 2

bwhencT

bwhendNeXT rT

=

=

0

0),( 2

bwhenpT

bwhendNeXT rT


20/234

Page 14

Options in CQG

Implied volatility

To find implied volatility the following equations should be solved for the value of sigma:

Call

Put

where

This equation has no closed form solution, which means the equation must be numerically

solved to find .

Bourtovs Model

Bourtovs model is based on the Black-Scholes model. It defines a special method to calculatevolatility, which is an input parameter of the Pricing Model Calculator.

)()( 21)(

dNeXdNeSc TrTrb =

)()( 1)(

2 dNeSdNeXp TrbTr =

( )T

TbXSd

+=

2/)/ln( 2

1

Tdd = 12


21/234

Page 15

Options User Guide

Cox-Ross-Rubinstein Model

The Cox-Ross-Rubinstein binomial model can be used to price European and American options

on stocks without dividends, stocks and stock indexes paying a continuous dividend yield,futures, and currency options.

TheoV

The main binomial model assumption is the underlying price can either increase by a fixed

amount uwith probabilityp, or decrease by a fixed amount dwith probability 1-p. So the

underlying price at each node is set equal to

where

S underlying price;

u, d up and down jump sizes that underlying price can take at each time step.

Option pricing is done by working backwards, starting at the terminal date. Here we know allthe possible values of the underlying price. For each of these, we calculate the payoffs from the

derivative, and find what the set of possible derivative prices is one period before. Given these,

we can find the option one period before this again, and so on. Working ones way down to theroot of the tree, the option price is found as the derivative price in the first node.

Call

At expiration date:

where n number of time steps.

At each previous step:

European exercise

American exercise

where

price up movement size;

price down movement size;

size of each time step;

up movement probability;

b the cost-of-carry, defined as:

b = r to price European and American options on stocks;

jiduS iji ,...,1,0, =

niXduSf inini ,...,1,0),0,max(, ==

[ ]1,1,1, )1( +++ += jijitrji fpfpef

[ ]( )1,1,1, )1(,max +++ += jijitrijiji fpfpeXduSf

= teu

== ued t /1

nTt /=

=

du

dep

tb


22/234

Page 16

Options in CQG

b = r q to price European and American options on stocks and stock indexes paying acontinuous dividend yield q;

b = 0 to price European and American options on futures;

b = r rf to price European and American currency options (rf risk-free rate of theforeign currency).

Put

At expiration date:

At each previous step:

European exercise

American exercise

Delta

Given the values calculated for the price, Delta approximation is

Gamma

Gamma approximation is

Theta

Theta can be approximated as

Vega, Rho

System uses the numerical differentiation to calculate the Greeks.

Implied volatility

System numerically finds implied volatility.

niduSXp inini ,...,1,0),0,max(, ==

[ ]1,1,1, )1( +++ += jijitrji fpfpef

1,1,1, )1(,max +++

+= jiji

triji

ji fpfpeduSXf

jif ,

dSuS

ff

S

f

=

= 0,11,1

( ) ( )( )22

2

0,21,2

2

1,22,2

2

2

5.0 dSuS

dSduSffduSuSff

S

f

=

=

t

ff

=

2

0,00,2


23/234

Page 17

Options User Guide

Garman-Kohlhagen Model

This model, developed to evaluate currency options, considers foreign currencies analogous to a

stock providing a known dividend yield. The owner of foreign currency receives a dividendyield equal to the risk-free interest rate available in that foreign currency. The model assumes

price follows the same stochastic process presumed in the Black-Scholes model.

This model is used to evaluate options written on currencies. The interest rate of the nativecurrency is used as the default, but you can set the foreign interest rate inModel preferences.

This model corrects the difference between native and foreign interest rates. However, as a

modification of Black-Scholes model, it possesses all its limitations.

Notation



Underlying price

Strike price

Interest rate

Interest rate in the foreign country

Time to expiration in years

Volatility

The European call price is given by:

Where:

The Europeanput price is given by:

C

P

U

E

r

fr

t

)()( thNEehNUeC rttr

=

t

trrEUh

f

)2/()/ln( 2++=

)()( htNEehNUeP rttrf +=


24/234

Page 18

Options in CQG

Merton Model

In 1973, Merton produced a model with a non-constant interest rate. He assumed that interest

rates follow a special type of random process.

By taking into consideration the dynamic process of interest rate determination, and thecorrelation between the underlying price and the options price, this model provides an

improvement over the Black-Scholes model. This model is generally used to value Europeanoptions written on stocks.

Notation



Underlying price

Strike price

Time to expiration in yearsCumulative normal density function

Volatility

Volatility of an interest rate contract

Interest rate

Correlation between the underlying and interest rate contracts

The theoretical values for European calls and puts are:

Where:

C

P

U

E

t)(xN

p

)(tR

)()()( thENtBhUNC =

)()()( htENtBhUNP +=

t

ttBXUh

2/)()(ln)/ln( +=

+=t

pp dtt0

22 )2()(

ttRetB

)()( =


25/234

Page 19

Options User Guide

Whaley Model

The quadratic approximation method by Baron-Adesi and Whaley (1987) can be used to price

American options.

TheoV

Call

where

b the cost-of-carry rate;

b = r to price options on stocks.b = r q to price options on stocks and stock indexes paying a continuous dividend yield q

b = 0 to price options on futures.

b = r rf to price currency options (rf risk-free rate of the foreign currency).

CGBS the generalized Black-Scholes call TheoV expression;

S* the critical commodity price for the call option that satisfies

The last equation should be numerically solved to find S*.

Put

+=

**

****

11)/(),,,,,(

SSwhenSX

SSwhenSSAbrTXSPp

q

GBS


26/234

Page 20

Options in CQG

where

PGBS the generalized Black-Scholes put TheoV expression;

S** the critical commodity price for the put option that satisfies

The last equation should be numerically solved to find S**.

Delta

Call

where

GBS- the generalized Black-Scholes call expression.

Put

where

GBS- the generalized Black-Scholes put expression.

( )[ ])(1 **1)(1

**

1 SdNeq

SA

Trb =

2

/4)1()1( 2

1

KMNNq

+=

( )[ ])(1),,,,,( **1)(1

****** SdNe

q

SbrTXSPSX TrbGBS =

+=

**

****1

11

1

)/(),,,,,( 11

SSwhen

SSwhenSSqAbrTXS qq

GBS


27/234

Page 21

Options User Guide

Gamma

Call

Put

Vega

Call

Put

Theta

Call

where


Put

where


+=

**

****2

111

0

)/()1(),,,,,( 11

SSwhen

SSwhenSSqqAbrTXS qq

GBS

=

**

**

0 SSwhen

SSwhenationdifferentiNumericalVega

= **

**

0 SSwhenSSwhenationdifferentiNumerical


28/234

Page 22

Options in CQG

Rho

Call

where


Put

where


Implied volatility


Implied volatility cant be calculated for call option if option value is less than (underlying price

- strike).

Implied volatility cant be calculated for put option if option value is less than (strike -

underlying).

=

**

**

0 SSwhen

SSwhenationdifferentiNumerical


29/234

Page 23

Options User Guide

Exotic Option Models

For further reading, we suggest:

The Complete Guide to Option Pricing Formulas. ISBN 0071389970.

Barrier Options,Binary/Digital Options,andLookback Optionsat www.global-derivatives.com.

Standard (Vanilla) Barrier

There are two kinds of the barrier options:

In = Paid for today but first come into existence if the underlying price hits the barrier Hbefore expiration.

Out = Similar to standard options except that the option is knocked out or becomesworthless if the underlying price hits the barrier before expiration.

TheoV

In Barriers

Down-and-in call

c(X>=H) = C + E = 1, = 1

c(X=H) = A + E = -1, = 1

c(X=H) = B C + D + E = 1, = -1

p(X=H) = A B + D + E = -1, = -1

p(X=H) = A C + F = 1, = 1

c(X


30/234

Page 24

Options in CQG

Up-and-out call

c(X>=H) = F = -1, = 1

c(X=H) = A B + C D + F = 1, = -1

p(X=H) = B D + F = -1, = -1

p(X


31/234

Page 25

Options User Guide

K possible cash rebate,

b the cost-of-carry.

b = r to price options on stocks.

b = r q to price options on stocks and stock indexes paying a continuous dividend yield q



Delta, Gamma, Vega, Theta, Rho

The system uses the numerical differentiation to calculate the Greeks.

Implied volatility

The software shall numerically find implied volatility.

2

2 2

r+=


32/234

Page 26

Options in CQG

Asset-or-Nothing Binary

At expiry, the asset-or-nothing call option pays 0 if S X. Similarly, a put

option pays 0 if S >=X and S if S < X.

TheoV

Call

Put

where

b the cost-of-carry.

b = r to price options on stocks.

b = r q to price options on stocks and stock indexes paying a continuous dividend yield q



Delta

Gamma

)()( dNeSc Trb =

)()( dNeSp Trb =

2

ln( / )

2

S X b T

dT

+ +

=

( )

( )

( )( ( ) )

( )( ( ) )

b r T

call

b r T

put

n de N d

T

n de N d

T

= +

=

( )

( )

( )(1 )

( )(1 )

b r T

call

b r T

put

de n d

T

S Td

e n dT

S T

=

=


33/234

Page 27

Options User Guide

Vega

Theta

Rho

Implied volatility

To find implied volatility the following equations should be solved for the value of sigma:

Call

Put

System numerically solves these equations.

( )

2

( )

2

ln( / )( )

2

ln( / )( )

2

b r T

call

b r T

put

T S X bT V Se n d

T

T S X bT V Se n d

T

+=

+=

( )

++

+=

2

/ln

2

)()()(

2)(

b

T

XS

T

dndNrbeS Trbcall

( )

++

=

2

/ln

2

)()()(

2)(

b

T

XS

T

dndNrbeS Trbput

( )

( )

( )0

( )0

( ) 0

( ) 0

b r T

call

b r T

put

rT

call

rT

put

Se n d T b

T

Se n d T b

T

STe N d b

STe N d b

=

=

= =

= =

)()( dNeSc Trb =

)()( dNeSp Trb =


34/234

Page 28

Options in CQG

Floating Strike Lookback

The Lookback models are used to price European lookback options on stocks without dividends,

stocks and stock indexes paying a continuous dividend yield and currency options.

A floating strike lookback call gives the holder of the option the right to buy the underlyingsecurity at the lowest price observed, Smin, in the life of the option. Similarly, a floating strike

lookback put gives the option holder the right to sell the underlying security at the highest priceobserved, Smax, in the options lifetime.

TheoV

Call

where

b the cost-of-carry;

b = r to price options on stocks;

b = r q to price options on stocks and stock indexes paying a continuous dividend yield

q;

b = r rf to price currency options (rf risk-free rate of the foreign currency);

Put

where

.

+

+=

)(2

2)()( 11

2

min

2

2min1

)(

2

aNeTb

aNS

S

beSaNeSaNeSc bT

b

rTrTTrb

T

TbSSa

++=

)2/()/ln( 2min

1

Taa = 12

+

+=

)(2

2)()( 11

2

max

2

1

)(

2max

2

bNeTb

bNS

S

beSbNeSbNeSp bT

b

rTTrbrT

T

TbSSb

++=

)2/()/ln( 2max1

Tbb = 12


35/234

Page 29

Options User Guide



Implied volatility

The system uses numerically find implied volatility.


36/234

Page 30

Options in CQG

Fixed Strike Lookback

In a fixed strike lookback call, the strike is fixed in advance, and at expiry the option pays out

the maximum of the difference between the highest observed price, Smax, in the optionlifetime and the strike X, and 0. Similarly, a put at expiry pays out the maximum observed

price, Smin, and 0.

TheoV

Call

when X > Smax

where

b the cost-of-carry;

b = r to price options on stocks;

b = r q to price options on stocks and stock indexes paying a continuous dividend yieldq;

b = r rf to price currency options (rf risk-free rate of the foreign currency);

when X =Smin

+

+=

)(2

2)()( 11

22

21

)(2

dNeTb

dNX

S

beSdNeXdNeSc

bT

b

rTrTTrb

T

TbXSd

++=

)2/()/ln( 2

1

Tdd = 12

+

++=

)(2

2)()()( 11

2

max

2

2max1

)(

max

2

eNeTb

eNS

S

beSeNeSeNeSXSec

bT

b

rTrTTrbrT

T

TbSSe

++=

)2/()/ln( 2max1

Tee = 12

+

+=

)(2

2)()(

11

22

1

)(

2

2

dNeTb

dNX

S

beSdNeSdNeXp bT

b

rTTrbrT


37/234

Page 31

Options User Guide

where

By defining the following variables all four formulas can be combined into one:

- option type adjustment,

Now the formulas transform into:



Implied volatility

The systems finds implied volatility numerically.

+

++=

)(2

2)()()( 11

2

max

2

2min1

)(

min

2

fNeTb

fNS

S

beSfNeSfNeSSXep

bT

b

rTrTTrbrT

T

TbSSf

++=

)2/()/ln( 2

min1

Tff = 12

z

=

optionput1

,optioncall1z

observed,extremepriceS

=option;putagcalculatinif,

option,callagcalculatinif

min

max,

S

SS

,limitpriceLS

=otherwise;,

puts,fororcallsforif,

X

XSXSSSL

( )

+=

=

+

+

++=

TbdN(zS/S)dN(ze

b

S)dN(zSXSez

)dN(zeT

bdzN

S

S

b

eSz

)dN(zeSz)dN(zeSzX)(SezTheoV

b

L

bT

LL

rT

bT

b

rT

rTr)T(b

L

rT

L

2

2

2

2

1

2

1

2

2

11

2

max

2

21

2

2


38/234

Page 32

Options in CQG

Interest-Rate Option Models

For further reading, we suggest The Complete Guide to Option Pricing Formulas. ISBN

0071389970.

The Vasicek Model

The Vasicek (1977) model is a yield-based one-factor equilibrium model. The model allowsclosed-form solutions for European options on zero-coupon bonds.

TheoV

Call

Put

where

L bond principal (i.e. face value),

bond time to maturity,

,

,

P(T)-the price at time zero of a zero-coupon bond that pays $1 at time T,

wherer the initial risk-free rate

)()( pT hNPXhNPLc =

)()( hNPLhNPXp pT +=

)(TPPT=

)(

PP =

2ln

1 p

Tp XP

PLh

+

=

dp =

( ) ( )a

ee

ad

aTTa

2

11

1 2)(

=

rTBeTATP

= )()()(

a

eTB

aT=

1)(

( )( )

=

a

TB

a

baTTBTA

4

)(2/)(exp)(

22

2

22


39/234


40/234

Page 34

Options in CQG

Call

Put

Implied volatility


( ) ( ) ( ) ( )p

TpTpTT

p

T

T

BBhnPXhNBPXhNBPL

BBhnPL

r

c

+

=

=

( ) ( ) ( ) ( ) pT

pTpTTp

T BB

hnPXhNBPX

BB

hnPLhNBPLr

p

+

+=

=


41/234

Page 35

Options User Guide

The Hull and White Model

The Hull and White (1990) model is a yield-based no-arbitrage model. This is extension of the

Vasicek model. The model allows closed-form solutions for European options on zero-couponbonds.

TheoV

Call

Put

Where


bond time maturity,

,

,

P(T) - the price at time zero of a zero-coupon bond that pays $1 at time T,

a the speed of the mean reversion.

Unlike Vasicek model, PTand Pare input parameters.

Delta

Call

Put

)()( pT hNPXhNPLc =


)(TPPT=

)(

PP =

2)(

)(ln

1 p

p XTP

PLh

+

=

( ) ( )aeea

aT

Tap

211

2

)(

=

( ) ( ) ( )TppppT P

hnPLhNXhnXP

c

=

=

11

( ) ( ) ( )Tp

p

p

p

T PhnPLhNXhnX

P

p

++=

=

11


42/234

Page 36

Options in CQG

Gamma


Vega

Because

Theta

Call

Put

where

( ) ( )Tp

p

pTpT P

hhnX

h

P

hnPL

P 22

11

+

=

=

( ) ( )xnxn =

( ) ( )

hhnPX

hhnPL

pcVega pT

p +

=

=

=

+

+

+

+=

=

p

ppTpT

p

p

rghnPXhNPrX

rghnPL

T

c

'

2

1)()('

2

1)(

=

XP

PLg

Tp

ln

12

( )TPT

r ln1

=

+

++

+

++=

=

p

p

p

ppTpT

rghnPL

rghnPXhNPrX

T

p

'

2

1)('

2

1)()(

( ) ( )( )

+

=

aT

TaaTaTTa

p

ea

ee

a

ee

2

)(22)(

12

1

2

1'


43/234

Page 37

Options User Guide

Rho

Since, the price at time zero of a zero-coupon bond that pays $1 at time t is

then

Call

Put

Implied volatility

The system finds implied volatility numerically.

rtetP

=)(

TT PTP =

PP =

p

Th

=

( ) ( ) ( ) ( )p

pTpT

pT

ThnPXhNTPXhNPL

ThnPL

r

c

+

=

=

( ) ( ) ( ) ( )p

pTpT

p

ThnPXhNTPX

ThnPLhNPL

r

p

+

+=

=


44/234

Page 38

Options in CQG

The Ho and Lee Model

Ho and Lee (1986) model is the no-arbitrage model. The model allows closed-form solutions for

European options on zero-coupon bonds.

TheoV

Call

Put

Where


bond time maturity,

,

,

P(T) - the price at time zero of a zero-coupon bond that pays $1 at time T,

The distinctions from Vasicek model are

- PTand Pare input parameters,

- pexpression is different.

Delta

Call

Put

)()( pT hNPXhNPLc =


)(TPPT=

)(

PP =

2)(

)(ln

1 p

p XTP

PLh

+

=

( ) TTp =

( ) ( ) ( )Tp

p

p

p

T PhnPLhNXhnX

P

c

=

=

11

( ) ( )2 21

1 pT p T p p T

h hL P n h X n h

P P P

= = +


45/234

Page 39

Options User Guide

Gamma


Vega

Because

Theta

Call

Put

where

,

( ) ( )

+

+=

=

pTp

p

pTpT P

hnX

P

hnPL

P

11

111

12

( ) ( )xnxn =

( ) ( )

hhnPX

hhnPL

pcVega pT

p +

=

=

=

+

+

+

+=

=

p

ppT

pT

p

p

rghnPX

hNPrXr

ghnPLT

c

'2

1)(

)('2

1)(

=

XP

PLg

Tp

ln

12

( )TPT

r ln1=

++++=

=

p

p

p

ppTpT

rghnPL

rghnPXhNPrX

T

p

'2

1)(

'2

1)()(

[ ]TT

p 32

' =


46/234

Page 40

Options in CQG

Rho

Since the price at time zero of a zero-coupon bond that pays $1 at time t is

then

Call

Put

Implied volatility

The system finds implied volatility numerically.

rtetP

=)(

TT PTP =

PP =

p

Th

=

( ) ( ) ( ) ( )p

pTpT

pT

ThnPXhNTPXhNPL

ThnPL

r

c

+

=

=

( ) ( ) ( ) ( )p

pTpT

p

ThnPXhNTPX

ThnPLhNPL

r

p

+

+=

=


47/234


48/234

Page 42

Options in CQG

, and is calculated by the formula above than may be expressed as

,

which is exactly identical to BS equation. Similar is true for . That also implies that some of

Greeks can be calculated by the corresponding BS formulas.

Prior to giving formulas for Greeks lets introduce a few helper equations which may help inimplementing the formulas found across the section.

, thus simplifying .

Put-call parity in Kirks model is expressed as:

.

Below are some partial derivatives used in equations

.

The first derivative of sigma by the price of the second futures is:

.

The second derivative of sigma by the price of the second futures is a bit more complex and is:

.

Partial derivatives of by the price of the second futures are also useful to have. Those are:

,

.

Also, some partial derivatives of the combined volatility are as follow:

,

,

c

)()( 21 dNXedNSecc TrTr

BS

==

p

=XF

F

+

2

22

122

1 2+=

( )12 FXFecp rT ++=

( ) 111

2

1

1

=

=

TF

F

d

F

d

( )22

12

2 XF

X

F +

=

( )

( ) ( )

+++

+

+

=

2

21

2

2

3

2

2

2

2

2

2

2

F

XF

XF

X

XF

X

F

21,dd

( )XFTd

FF

d

+

=

2

2

22

1 11

( )XFTd

FF

d

+

=

2

1

22

2 11

= 1

1

=

2

1

2


49/234

Page 43

Options User Guide

.

Finally it should be noted that

,

and hence:

.

Delta1, Delta2

Each delta is calculated with respect to the corresponding asset price movement. Sensitivity of

call option price to price change of the first futures is:

.

Sensitivity of call option price to price change of the second futures is:

.

By virtue of call-put parity given above the following expressions are true for put option Deltas.Sensitivities of put option price to price change in price of either the first or the second futures

are, respectively:

,

.

Gamma1, Gamma2

Each gamma is calculated similar to delta, with respect to the corresponding asset pricemovement.

The equation is identical for call and put:

The gamma with respect to the second futures price is identical for call and put and isexpressed as:

.

1=

0/)()( 21 = Fdndn

)()( 21 dndnF =

( )11

1 dNeF

c rTc =

=

( ) ( )

++=

=

2

222

2

2 )(F

TdnXFdNeF

c rTc

rTcp eF

p =

=

11

1

rTcp eF

p +=

= 2

2

2

( )[ ] ( )[ ] ( )TFdnedTdn

FdTdn

TFe rTrTpc

1

122112

1

11 11 =

++==

( ) ( )

++

+

==

22

222

2

2

2

22

2222

FF

dd

FXF

FT

F

ddne

rTpc


50/234

Page 44

Options in CQG

Vega

The vega is chosen to reflect sensitivity of the spread price with respect to movement of value

of the combined volatility :

.

Theta

Call

,

Put

,

where

Rho

Call

Put

Chi

Chi (as defined in Carmona & Durrleman) denotes the first derivative of option price by

correlation coefficient .

.

TdneFVega rT = )( 11

gcr +=

gpr +=

( ) ( )

( ) ( )

( ) ( 1122212 22ln

2

ln

22 dnT

FednT

XFeT

FdnT

FdnFeT

XFg

TrTrTr

=

+=

++

+=

cT=

pT=

( )

2112 dnTFFe

c Tr =

=


51/234

Page 45

Options User Guide

Implied Volatility & Correlation

There is no definite way to calculate both 1, 2given a concrete spot price. It is supposed to

determine the value of the combined volatility by the standard approach of solving theequation numerically as done in Black-Scholes model.

However, it should be possible to calculate implied value of any of three 1, 2, variablesprovided the other two are known. For that purpose the partial derivatives of option value byany of three variables may be required to apply Newtons equation solver, for instance.

Lets denote a selected variable as , which may be either of 1, 2, . The generic form of the

partial derivative of option value is:

.

The expression demonstrates that values calculated with BS model can be used. Substituting

with 1, 2, and the expressions for each of , and can be obtained using the

corresponding partial derivatives of given earlier.

c

( )

=

=

=

11111 Vega

cTdnFe

c BSTr

21

,

ccc


52/234

Page 46

Options in CQG

Cumulative Normal Distribution FunctionApproximation

For further reading, we suggest: The Complete Guide to Option Pricing Formulas. ISBN 0071389970.

Handbook of Mathematical Functions. ISBN 0486612724.

Abromowitz and Stegun approximation

The following approximation of the cumulative normal distribution function N(x) producesvalues to within six decimal places of the true value.

When x >= 0

N(x) = 1 n(x)(a1 * k + a2 * k^2 + a3 * k^3 + a4 * k ^ 4 + a5 * k ^5)

when x < 0

N(x) = 1 N(-x)

where

n(x) normal distribution;

k = 1 / (1 + 0.2316419 * x);

a1 = 0.319381530;

a2 = -0.356563782;

a3 = 1.781477937;

a4 = -1.821255978;

a5 = 1.330274429;

Harts approximation

This algorithm uses high degree rational functions to obtain the approximation. This function is

accurate to double precision (15 digits) throughout the real line.


53/234

Page 47

Options User Guide

Numerical Methods for Solving Equations

The system offers several methods of the solving of the nonlinear equations.

For further reading, we suggest Numerical Recipes: The Art of Scientific Computing, 3rded.

ISBN-10: 0521880688.

Bisection Method

The bisection method is a simple iterativeroot-finding algorithm.

The methodconvergence is linear,which is quite slow. On the positive side, the method isguaranteed to converge.

Newtons Method

Newton's method, also called the Newton-Raphson method, is an iterativeroot-finding

algorithm.

The methodconvergence is usually quadratic,however it can encounter problems for functionwith local extremes.

Newton's method requests that function isdifferentiable.

Newton Safe Method

Newton Safe method is an iterativeroot-finding algorithm,which combines the bisection and

Newtons methods.

The method, however if function has local extremes convergence can be linear.

Like Newton's method, Newton safe method requests that function isdifferentiable.

Brents Method

Brents method is an iterativeroot-finding algorithm.

This method is characterized by quadratic convergence in case of smooth functions and

guaranteed linear convergence in case of non-smooth or sophisticated functions.
http://en.wikipedia.org/wiki/Root-finding_algorithmhttp://en.wikipedia.org/wiki/Rate_of_convergencehttp://mathworld.wolfram.com/Root-FindingAlgorithm.htmlhttp://mathworld.wolfram.com/Root-FindingAlgorithm.htmlhttp://en.wikipedia.org/wiki/Rate_of_convergencehttp://en.wikipedia.org/wiki/Derivativehttp://mathworld.wolfram.com/Root-FindingAlgorithm.htmlhttp://en.wikipedia.org/wiki/Rate_of_convergencehttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Root-finding_algorithmhttp://en.wikipedia.org/wiki/Root-finding_algorithmhttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Rate_of_convergencehttp://mathworld.wolfram.com/Root-FindingAlgorithm.htmlhttp://en.wikipedia.org/wiki/Derivativehttp://en.wikipedia.org/wiki/Rate_of_convergencehttp://mathworld.wolfram.com/Root-FindingAlgorithm.htmlhttp://mathworld.wolfram.com/Root-FindingAlgorithm.htmlhttp://en.wikipedia.org/wiki/Rate_of_convergencehttp://en.wikipedia.org/wiki/Root-finding_algorithm


54/234

Page 48

Options in CQG

Numerical Differentiation

The first derivative shall be calculated as

The first derivative represents instantaneous rate of change, which is limit of average rate ofchange where h is the small time interval,

h=the time between point t and point t+1=t (delta t)The secondderivative shall be calculatedas

h

ff

dx

df ii

xx i2

11 +

=

2

11

2

2 2

h

fff

dx

fd iii

xx i

+

+


55/234

Page 49

Options User Guide

Trading Options

Trading with CQG IC is explained in detail in ourtrading user guide.

As an options trader, you may want to:

Add a Greek column to DOMTrader (Trading Preferences > Display > Greek column foroptions)

Highlight theoretical value on the DOMTrader (Trading Preferences > Display > PriceColumn)

Select on options model (Trading Preferences > Display > Options)

Use theoretical value to calculate UPL/MVO (Trading Preferences > Display > Status)

DOMTrader and Order Ticket have options-specific components. The current strike price is

displayed, and you can change the model and Greeks directly on the trading application. The

Account Summary area of Orders and Positions also has options-specific data.

Note about options prices on DOMTrader

You may wonder why price calculations sometimes differ between the options window andDOMTrader.

As expected, the price on the options window is calculated using market data and shows the

current value of the Greek for a single price.

DOMTrader offers an entire ladder of prices. Except for the single cell where the last tradeoccurred, other prices are potential prices at which the options contract may be traded later, ifthe market moves in that direction. Because we cannot calculate an actual price for a future

state, we use predictive mathematics to derive those potential prices.

To calculate Delta for a potential price of C.EP U213350 away from the current market (say, at4100), we use the price of the underlying instrument F.EPU2 and other characteristics of the

F.EP market movement that would result in market of C.EP U213350 moving to 4100.

Thus, we are trying to predict what the value of Delta would be then if the option price achieves4100. CQG uses a complex algorithm to make that prediction.
http://www.cqg.com/Docs/Trading_UG.pdf#page=1http://www.cqg.com/Docs/Trading_UG.pdf#page=1http://www.cqg.com/Docs/Trading_UG.pdf#page=1http://www.cqg.com/Docs/Trading_UG.pdf#page=1


56/234

Page 50

Options in CQG

Because of this difference in calculation, the prices on the options window may be differentfrom the prices on DOMTrader.


57/234

Page 51

Options User Guide

Setting Options Preferences

To set options preferences, click the Setupbutton and then click Options Preferences. Youcan also click the Prefsbutton on the Options toolbar.

To start, select the model and where to apply these preferences. If you select DDE & Operatorvalues, changes apply to other areas where options are used, such as custom studies.

Click the Summarybutton to view, print, and save (.dat file) the current settings.

Click the Defaultsbutton to return to default values.


58/234

Page 52


Other Options preferences include (tabbed area at bottom of window):

View settings allow you to show or hide Greek and implied volatility scales, ordercolumns, and set extended coloring parameters.

Volatility settings allow you to set the implied volatility type, evaluation method foraverage volatility, and select a volatility calculation type.

Interest Rate settings allow you to set the interest rate for various currencies.

Price Filter settings allow you to select which price to use for underlying and option.You can also choose to use most recent settlement prices.

Greeks Scale settings allow you to set the price scale, time direction, and time scaleand to choose percent or fractions for implied volatility and delta and gamma.

Advanced settings allow you to select the underlying contract type and increase days toexpiration.

Model settings allow you to define parameters for each model.

Update Frequencysettings allow you to set the refresh period for average volatility,interest rate, and new/removed contract and to set update delays for theoretical value

and the Greeks.


59/234

Page 53

Options User Guide

Setting Options Window View Preferences

View settings allow you to show or hide Greek and implied volatility scales, order columns, and

set extended coloring parameters for old and stale.

Appearance

Select this check box to display the scale setting (percent or fraction) in the header.

Column order

Click the Monthscheck box to arrange the columns by month.

Click the Puts/Callscheck box to arrange the columns so that all calls columns come beforeputs columns.

Extended Coloring: Mark as

Set the threshold for old prices and stale movement.


60/234

Page 54


Setting Options Calculator View Preferences

Degree of Polynomial

Enter a value up to 8. The higher value, the slower the drawing of the graph but the better thecurve fits the Volatility Skew graph.

Points to Plot

Enter a value up to 120. The higher the number, the slower the drawing of the graph but the

higher the definition.


61/234

Page 55

Options User Guide

Setting Volatility Workshop View Preferences

Show

Choose the elements to add to the Volatility Workshop display: Yesterday curve, Yest. IVs,

Call/Put curve, or Net Change.

Each of these becomes an additional row in the table about the graph and are displayed on thegraph.

The curves are added to the graph. Yesterdays IV (each options settlement IV) is representedas circles on the graph. Net change is represented as a vertical line between the current IV and

yesterday's settlement IV.

Strikes Range

Expand the curves on the left and right side by a designated percentage. This facilitates

estimating the IVs of options that have not yet been listed. For example, if the range prior to

the expansion was from 1000 to 3000 and the range was expanded on the right side by 10percent, the new range would be from 1000 to 3200 [(.1*(3000 - 1000) + 3000].


62/234

Page 56


X-Axis type

Select the variable represented by the X-axis: Strike Priceor Delta.

Mark as

Set the threshold for old prices, in hours, and stale movement, in percent.


63/234

Page 57

Options User Guide

Setting Strategy Analysis View Preferences

Display type

Select whether to display the P&L graph using profit/loss as a function of the underlying price orvalue of the portfolio as a function of price.


64/234

Page 58


Setting Volatility Preferences

Volatility settings allow you to set the implied volatility type, evaluation method for average

volatility, and select a volatility calculation type.

Volatility for calculation

Select one of:

Apply vol surface= 3-D value from the Volatility Workshop

Apply vol curve= 2-D value from the Volatility Workshop

Use IV for Greeks&TheoV = Used in conjunction with the Implied Volatility Type,Traded or Momentary.

Use IV for Greeks= Used in conjunction with the Implied Volatility Type, Traded orMomentary.

Use Average Vol= Used in conjunction with the Average Volatility evaluation method.

The average volatility using Put-Call Separate and Put-Call Combined is calculated bytaking a weighted average of the 2 implied volatilities for the strikes encompassingthe at-the-money-strike.

For example, with the underlying at 1392.00 and the implied volatility of the 1390.00calls at 26.02 and the implied volatility of the 1395.00 calls at 25.42 the average callvolatility would be: .6(26.02) + .4(25.42) = 25.78. This volatility would be used to

value all the calls. The average put volatility would be calculated the same way and

that value would be used to value the puts. If the Put-Call Combined choice wereselected, the call volatility and put volatility would be averaged and that volatility

would be used for all the options series of that particular underlying.

Please note that theoretical value cannot be calculated using implied volatility. If you select the

Use implied volatilitycheckbox, CQG uses implied volatility to calculate all the values excepttheoretical value, where it uses one of the selections from the dropdown list: Put-Call Separate,Put-Call Combined or Historical. However, if the Use implied volatilitybox is not selected, all

the values are calculated using one of the three methods.


65/234

Page 59

Options User Guide

Implied Volatility Type

Select one of:

Traded= Matches the options price with the underlying price, based on a time whenthe two prices were in sync, that is, the options price happened no later than 3 hours

after the underlying price. This could lead to a value that is in sync but not current.

Using this value involves taking the synced underlying price (also referred to as thecoherent underlying price), which is the close of the underlying instrument during

the minute prior to the last option tick. However, if the underlying has not tradedduring this minute, the system uses the underlying tick closest to the time of the

option trade, as long as it happened during the current trading day. If the options

price is a closing value, the settlement price for the underlying is used as thecoherent underlying price.

Momentary= Matches the options tick with the nearest tick in the underlying, even ifthe underlying trade happened after the options price. Volatilities calculated this waymay be off by a large amount if the underlying trade took place substantially before orafter the options trade.

If you select this value, the calculation uses the most current underlying price andthe most current options price. Volatilities calculated this way may be off by a largeamount, if the underlying price has changed significantly since the last options tick.

In other words, momentary implied volatility takes the most current underlying tick

without matching it to the time of the options. This may or may not result in thesame volatility as the traded implied volatility.

These selections are global, which means they apply to all models. (Implied volatility selections

made on the Modeltab are only relevant to the selected model.)

Average volatility

Select one of:

Put-Call Separate= Two values, one for the calls and one for the puts, are calculatedand given separately. These values are then used as the volatility input for the selectedoptions model.

Put-Call Combined= The separate call and put volatilities are averaged together andone value is given. This value is then used as the volatility input for the selected optionsmodel.

Historical Volatility= Represents the standard deviation of a series of price changesmeasured at regular intervals. You define the Historical Volatility using either Percent or

Logarithmic price changes. Percent changes assume that prices change at fixed

intervals. Logarithmic changes assume that prices are continuously changing. Historical

Volatility requires a period value. Constant value requires a percentage value. Constant Volatility= If selected, you must also select a percentage for the volatility.

For example, if the selected contract was trading at 1300 and the volatility valueselected was 10%, you would be implying an underlying price of 1300+ or - 10%, i.e.,1170-1430 over the next year.


66/234

Page 60


Setting Interest Rate Preferences

These settings allow you to set the interest rate for various currencies.

First, select the currency using the drop down menu, then select the type of interest rate andset the value.


67/234

Page 61

Options User Guide

Setting Price Filter Preferences

These settings allow you to select the options and underlying prices that are used for the

options displays. You can also choose to use most recent settlement prices.

Use Most Recent Settlement Prices

When you click this button, the system disables the other choices and yesterday's settlement

price is used. If the market has already closed for the day, then today's settlement price isused.

Yesterday

Select this button to use yesterdays closing price.

No Filtering

Click this button to use the most current Bid, Ask, Last Trade, or Yesterday's Close as theoperative option price.

Option price and Underlying price

Select the price type for both the Option and the Underlying price: Bid, Ask, Bid/Ask

average, Last Trade, and Yesterdays Close.

If more than one price is selected, the system uses the most current of the selected prices.

For example, if only Last Trade and Yesterday's Close are selected, the last trade appears as

long as that trade took place in the current day's session. Likewise, if Bid or Ask is selected

along with Last Trade, the most recent Bid or Ask appears as long as it is more recent than thelast trade. If not, the last trade appears.


68/234


69/234

Page 63

Options User Guide

Setting Advanced Preferences

Advanced settings allow you to select the underlying contract type and increase days to

expiration.

Not all options are available for all models:

Black, Black-Scholes, Bourtov, and Garman-Kohlhagen Modifications only

Whaley Modifications and Dividends amount

Merton Modifications, Underlying contract type, Dividends amount

Cox-Ross-Rubinstein All

Contract style

Select Americanor European.

Underlying contract type

Select Futuresor Indices, Stocks, etc. or click the select automaticallycheck box.

Type a value for the percentage of the underlying price for the dividends amount.

Modifications

Type a value for how many days you want to increase the expiration by. You can also use the

arrows. This is useful for contracts that are deliverable or settle after the last trading day.


70/234


71/234

Page 65

Options User Guide

Setting Update Frequency Preferences

Because Greek values generally change slowly and updating them takes a lot of processing

time, CQG IC offers you the opportunity to set optimal update frequencies based on your

preferences.Update Frequency settings allow you to set the refresh period for average volatility, interest

rate, and new/removed contract and to set update delays for theoretical value and the geeks.

These preference do not apply to the Options Calculator.

Delayed updates for model values

This setting allows you to delay updates for particular model values. Select the check box, then

enter delays, in seconds, for the theoretical value; Delta & Gamma; and Vega, Theta, Rho.

If this check box is cleared, the system updates the Greek and Theoretical values whenever

there is a relevant change in the data.

Refresh period for

Enter refresh periods for Average Volatility, Interest Rate, and New/Removed Contracts.


72/234

Page 66


Updating the Refresh Rate

The refresh rate is different from the update frequency rates set in preferences. While

frequency rates dictate when calculations are updated, the refresh rate dictates when the

particular options window view is updated.

To change the update rate

1. Click the Setupbutton.

2. Click Update Rate.

3. Click the rate you want to set and enter a value for the interval. To stop updates,click the No updatesbutton.

4. Click OK.


73/234

Page 67

Options User Guide

Options Window

The Options Window has three views: Standard, Greek, and Theoretical versus Underlying. Youcan customize these views, so that they display information relevant to you.

To open the Options window, click the OptWndbutton on the toolbar. If the button is not

displayed, then click the Morebutton, and then click Options. You can also click the Options

button and then click Options Window.

The Options Window has three views:

Standard

Greek

Theoretical versus Underlying.

The Standard view changes based on the value you want displayed: LPrice, TheoV, Delta,

Gamma, Theta, Vega, IV, Open Int, and Volume.

The title bar indicates which view is active.


74/234

Page 68

Options Window

Standard view

Data in the top row includes:

UndPr= underlying price

DTE= number of calendar days until expiration

Exp= expiration date

Vol= default volatility used for calculations, default values is set in Options preferences:

IVS= implied volatility shift, sets the increase or decrease of all implied volatility values


75/234

Page 69

Options User Guide

IR= default interest rate calculated by taking 1 near term T-Bill price

Data in the bottom row includes the strike price, the bid or ask price, and then a value based

on your settings. For example, if the LPricebutton is selected, then this value is last price netchange. If the Thetabutton is selected, last price and theta is displayed.

In this example:

pink text = yesterday extended colors

red text = daily net down

green text = daily net up

Colors can bechanged.


76/234


77/234

Page 71

Options User Guide

Theoretical versus underlying (T/U) view

The T/U view displays data according to strike price.

Data in the top row includes:

UndPr= underlying price

DTE= number of calendar days until expiration

Exp= expiration date

Vol= default volatility used for calculations

IVS= implied volatility shift, sets the increase or decrease of all implied volatility values

IR= default interest rate calculated by taking 1 near term T-Bill price


78/234


79/234


80/234

Page 74

Options Window

Pause button

Pauses data updates and value recalculations.

Options displays constantly update during trading hours. Consequently, when the markets are

active, the displays could be changing quite rapidly, not allowing you to fully digest the effectsof each change. To alleviate this problem, you can pause without losing data.

Right-click this button to update the data immediately and update the rate.

Settle button

Click this button to view options data based on the most recent settlement price rather than themost recent tick data.

Prefs button

Click this button to open theOptions Preferenceswindow.

Cost button

Click this button to display the notional value of the option premium. Click it again to return to

the regular display. Works in conjunction with the multiplier button.

Multiplier button

Type a number to multiply the notional value of the option premium by. Displayed only whenthe Costbutton is on.


81/234

Page 75

Options User Guide

Customizing Columns

You are able to customize the columns displayed in the Greek view.


2. Click Customize Columns.

3. Select and clear the check boxes for the columns you want to show and hide.

4. To move the columns, use the Move to Top, Move Up, and Move Downbuttons.


82/234

Page 76

Options Window

Column Names

Column Label Full Name

Ask Ask Price

Ask Vol Ask Volume

Bid Bid Price

Bid Vol Bid Volume

Delta Delta

DeltaNC Delta Net Change

Gamma Gamma

GammaNC Gamma Net Change

Imp Vol Implied Volatility

ImpV NC Implied Volatility Net Change

Net Chg Net Change

OI Open Interest

Price Price

Pr-Theo Price - Theoretical Value

Rho Rho

Rho NC Rho Net Change

Theo NC Theoretical Value Net Change

TheoVal Theoretical Value

Theta Theta

ThetaNC Theta Net Change

TickVol Tick Volume

Time Time

Und Pr Underlying Price

Vega Vega

Vega NC Vega Net Change


83/234

Page 77

Options User Guide

Column Label Full Name

Volume Volume

Vol Crv Volatility Curve Value


84/234

Page 78

Options Window

Changing the Order of Columns

To toggle the order of the columns between months and puts/calls for the LPrice, TheoV, Delta,

Gamma, Theta, Vega and IV views:


2. Select Change Order. A months view changes to puts/calls and a puts/calls viewchanges to months.

Months view:

Puts/Calls view:


85/234


86/234

Page 80

Options Window

Changing the Display Type

In addition to changing the display of the standard view options window with the toolbar

buttons, you can right-click the Setupbutton and then click the display you want:


87/234

Page 81

Options User Guide

Opening Another Application from an OptionsWindow

Right-click the options window, and then click an application name, including: Time & Sales

Snap Quote

Chart

Options Calculator

Options Graph

Volatility Workshop


88/234

Page 82

Options Window

Setting What If Options Parameters

On the Options Parameterswindow, you can change any or all of several variables for

different series: Underlying Price, Volatility, Implied Volatility Shift, Interest Rate, Days to

Expiration (days until the most distant expiration selected in the Apply to area), and Date.

1. Click the WhatIfbutton. You can also right-click on the Options window.

2. Select the series to which the changes are applied from the Apply tocolumn. Clickthe All buttonto select every series in the selected commodity.

3. Enter the changes in the What ifcolumn.

Click the Newtab to create another What If set.

Click the Actualsbutton to clear any What Ifs that have been applied to the options window.


89/234


90/234

Page 84

Options Window

Placing Orders from the Options Window

1. Right-click on the options window.

2. Click Place an Order.

The Order Ticket, Simple Order Ticket, or DOMTrader opens depending on your

system settings. (Setup > System Preferences > Misc > Preferred Order Entry

Display).


91/234

Page 85

Options User Guide

Options Calculator

CQGdesigned the Options Calculator to calculate and display the theoretical and Greek valuesof an option contract based on user-defined What if values. You can display outputs for a singleset of What if values or in graphical form over a continuously varying range of What ifs.

To open the Options Calculator, click the OptCalcbutton on the toolbar to launch the Options

Calculator. If the button is not displayed, click the Morebutton, and then click Options

Calculator. You can also click the Optionsbutton and then click Options Calculator.


92/234

Page 86

Options Calculator

Options Calculator Components

The Options Calculator includes these areas:

Title bar

Contract area

Inputs area

Calculate area


93/234

Page 87

Options User Guide

Graph area


94/234

Page 88

Options Calculator

Options Calculator Toolbar

These buttons are common to both the options window and the options calculator:

Actuals

Puts

Calls

Prev/Next

Pause

Settlement

Prefs

The Options Calculator toolbar also includes these buttons:

FullScr button

Displays the Options Calculator graph across the entire width of the CQG window, hiding the

Contract and Input sections.

Rescale button

Re-adjusts the scales.

Futures button

Switches from an FX OTC view to a futures view.

FXOTC button

Click this button to view OTC Foreign Exchange contracts.

The CQG FX OTC Options Calculator allows users to evaluate several types of OTC cross

currency options. Currently users can evaluate 4 types of options: Vanilla OTC Spot, ExoticVanilla Barrier, Exotic Binary AON and Exotic Lookback.

To use the FX OTC Options Calculator, you must specify:

a model

underlying asset price

strike price

interest rate

volatility

days until expiration

specific model parameters.


95/234

Page 89

Options User Guide

When these values are given, the Options Calculator evaluates the theoretical value or impliedvolatility (if options price was specified) and all Greeks for the "virtual contract."


96/234

Page 90

Options Calculator

Using the Options Calculator

Using the [Tab]key (to move to the next cell) and[Shift] + [Tab]keys (to move to the

previous cell) keys facilitates moving around in the Options Calculator.

Using the Options Calculator involves:

1. Selecting the desired instrument symbol.

2. Inputting the desired series.

3. Selecting a model.

4. Inputting the What if values (if desired).

5. Choosing a type of graph (top tabs).

6. Selecting a view (bottom tabs).

Selecting a Symbol

To begin using the Options Calculator you must:

Enter the commodity symbol without any month indicator.

Example: JY

Selecting the Class and Expiration Month

Once you have entered the desired symbol, a drop-down list appears in the Option row of the

Contract section.

Select the desired class and expiration month from the drop-down list associated with the

Option row in the Contract section.

Selecting the Strike

After you have selected a symbol, class and expiration month, a drop-down list appears in the

Strikerow.

Select the desired strike price.

After a series is selected, the Actualscolumn is filled in with the most recent values.

Note: Prices indicated by an asterisk in the Actuals column are yesterday's values.


97/234

Page 91

Options User Guide

Selecting a Model

Options pricing models produce theoretical values for an option contract based on five inputs:

Underlying Price, Strike Price, Time