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8/2/2019 Option Contract (Imran)
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8/2/2019 Option Contract (Imran)
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In finance, an option is a derivatives financial instruments that specifies a
contract between two parties for a future transaction on an asset at a
reference price (the strike).The buyer of the option gains the right, but not
the obligation, to engage in that transaction, while the seller incurs the
corresponding obligation to full fil the transaction. The price of an option
derives from the difference between the reference price and the value of
the underlying asset (commonly a stocks, a bond, a currency or a futurecontract) plus a premium based on the time remaining until the expiration
of the option. Other types of options exist, and options can in principle be
created for any type of valuable asset.
Option
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Types of Option
Exchange-traded options
It is(also called "listed options") are a class of exchange traded
derivatives. Exchange traded options have standardized contracts, and
are settled through a Clearing House with fulfillment guaranteed by
the credit of the exchange. Since the contracts are standardized,
accurate pricing models are often available. Exchange-traded options
include:
Stock Option,
Bond Option and Other Interest Rate Option
Stock Market Index Option or, simply, index options and
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Over the Counter Option
It is(OTC options, also called "dealer options") are traded between
two private parties, and are not listed on an exchange. The terms of an
OTC option are unrestricted and may be individually tailored to meet
any business need. In general, at least one of the counterparties to an
OTC option is a well-capitalized institution. Option types commonly
traded over the counter include:
interest rate options
currency cross rate options
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Other option types
Another important class of options, particularly in the U.S.,
are employee stock option, which are awarded by a company to their
employees as a form of incentive compensation. Other types of options
exist in many financial contracts, for example real estate option are often
used to assemble large parcels of land, and prepayment options areusually included in mortgage loans. However, many of the valuation
and risk management principles apply across all financial options.
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European option an option that may only be exercised on expiration.
American option an option that may be exercised on any trading day
on or before expiry.
Bermudan option an option that may be exercised only on specified
dates on or before expiration.
Barrier option any option with the general characteristic that the
underlying security's price must pass a certain level or "barrier" before it
can be exercised.
Exotic option any of a broad category of options that may include
complex financial structures.[7]
Vanilla option any option that is not exotic.
Types of Option Styles
http://en.wikipedia.org/wiki/Option_(finance)http://en.wikipedia.org/wiki/Option_(finance)8/2/2019 Option Contract (Imran)
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Hedging risk with Derivatives
Review of equity options
Review of financial futures
Using options and futures to hedge portfolio risk
Introduction to Hedge Funds
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Options -- Contract
Calls and Puts
Underlying Security (Number of Units)
Exercise or Strike Price
Expiration date Option Premium
American, European, Asian, etc.
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Options -- Markets
1 Buyer + 1 Seller (writer) = 1 Contract
Examples of Price Quotations
Premium = Intrinsic Value + Time Prem
Options available on Equities
Indicies
Foreign Currencies
Futures
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Options -- Basic Strategies
Buy Call
Sell (write) Call
Buy Put
Sell (write) Put
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Options -- Advanced Strategies
Straddle
Strips and Straps
Vertical Spreads
Bullish Bearish
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Options - Determinants of Value
Value of Underlying Asset
Exercise Price
Time to Expiration
VOLATILITY Interest Rates
Dividends
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Options -- Black Scholes Option
Pricing Model C = SN(d1) - Xe
-rTN(d2)
ln(S/X) +(r+s2/2)Td1 = ---------------------------sT1/2
d2 = d1 - sT1/2
Put-Call Parity: P = C + Xe-rT - S
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Futures Contract
Agreement to make (sell) or take (buy) delivery of aprespecified quantity of an asset at an agreed upon price at aspecific future date.
ex. S&P 500 Index Futures:
Price: 1126.10; Delivery month: June
Buyer agrees to purchase a portfolio representing the S&P500 (or its cash equivalent) for $1126.10 x 250 = $281,525 onThursday prior to 3rd Friday in June. (Buyer is locking in thepurchase price for the portfolio.)
Seller agrees to deliver the portfolio described above.
Note: since this is a cash settled contract, if the price was1116.10 on the delivery date, the buyer would pay the seller$2,500 (= 10 x 250). If the price was 1136.10, the seller wouldpay the buyer $2,500
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Futures Contract: Marking to
Market Marking to market:
Price of Futures contract is reset every day
Gains/Losses versus previous day are posted to buyer and
seller margin accounts Futures = a bundle of consecutive 1-day forward contracts
If futures held to expiration, effective delivery price is sameas when contract initiated
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Futures Contract: Marking to
Market example (C$ contract)11/2 $0.7483 $2000
11/3 $0.7490 +$70 $2070
11/4 $0.7480 -$100 $1970
11/5 $0.7472 -$80 $1890
11/8 $0.7422 -$500 $1390 Add $610
11/9 $0.7430 +$80 $2080
11/10 $0.7432 +$20 $2100
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Speculators often sell index futures when they expect theunderlying index to depreciate, and vice versa.
Index Futures Market
1. Contract to sellS&P @ 1126.1
($281,525) on June17.
April 4
2. Buy S&P @ 1106.1($276,525) on spot
market and deliver @1126.1
June 17
3. Profit = $5,000
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Index futures may be sold by investors to hedge risk associatedwith securities held.
Index Futures Market
1.Contract to sell S&P @1126.1 ($281,525) on
June 17.
April 4
2. Market falls to1106.1.Gain =$5000
June 17
3. Gain offsets (approx.)loss of $5000 onsecurities held
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Most index futures contracts are closed out before theirsettlement dates (99%).
Brokers who fulfill orders to buy or sell futures contracts earn a
transaction or brokerage fee in the form of the bid/ask spread.
Index Futures Market
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Hedging with Derivatives
Basic option strategies
Covered call
Protective put
Synthetic short Basic futures strategies
Using interest rate futures to reduce risk
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Covered Call
Sell call on stock you own. (Long stock, short call)
Good: As value of stock falls, loss is partially offset by premium
received on calls sold.
Essentially costless since hedge generates a cash inflow
Bad: Maximum inflow from call = premium; Hedge is less
effective for large drop in stock price
If stock price rises, call will be exercised; Investor transfersgains on stock to holder of call.
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Protective Put
Buy put on stock you own. (Long stock, long put)
Good:
As value of stock falls, loss is partially offset by gain in valueof put. Gain from put continues to grow as stock price falls. If stock price rises, maximum loss on put = premium;
Investor keeps all stock gains less fixed put premium.
Bad: More expensive to hedge with put
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Synthetic Short
Sell call and buy put on stock you own. (Long stock, short call,long put)
Good: As value of stock falls, loss is offset by gain in value of put. Gain
from put continues to grow as stock price falls. If stock price rises, gain is offset by loss on call. Loss from call
continues to grow as stock price rises. Very effective hedging device Can be self-financing (premium received on put sold offsets
premium paid on call purchased)
Bad: Often more expensive than simply shorting the stock itself.
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Delta Hedging with Options
Call Delta = DC= dC/dS
From Black-Scholes model,DC = N(d1)
Ex.: If S=74.49, X=75, r=1.67%, s =38.4%,t=0.1589 yrs.
Then, C = 4.40 and N(d1) = 0.5197
If S increases by $1, C increases by $0.5197
Hedge Ratio = H = 1/DC = 1/0.5197 = 1.924
Sell 1.924 calls per share of stock held to hedge!
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Example of Call Hedge Held toExpiration, 1000 share stock position
IBM Profit S Profit C Combined90 15,510 -20,140 -4,63085 10,510 -10,640 -13080 5,510 -1,140 4,37075 510 8,360 8,870
74.49 0 8,360 8,36070 -4,490 8,360 3,87065 -9,490 8,360 -1,13060 -14,490 8,360 -6,13055 -19,490 8,360 -11,130
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Delta Hedging - Puts
Put Delta = DP= dP/dS From Black-Scholes model and Put-Call Parity,
DP= DC 1 =N(d1) - 1
Ex.: If S=74.49, X=75, r=1.67%, s =38.4%,t=0.1589 yrs.Then, C = 4.40, P = 4.71, N(d1) = 0.5197,and N(d1) -1 = -0.4803
If S increases by $1, P decreases by $0.4803Hedge Ratio = H = 1/D = 1/0.4803 = 2.082Buy 2.082 puts per share of stock held to hedge!
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Example of Put Hedge Held toExpiration, 1000 share stock position
IBM Profit S Profit P Combined90 15,510 -9,891 5,61985 10,510 -9,891 61980 5,510 -9,891 -4,38175 510 -9,891 -9,381
74.49 0 -8,820 -8,82070 -4,490 609 -3,88165 -9,490 11,109 1,61960 -14,490 21,609 7,11955 -19,490 32,109 12,619
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Delta Hedging with Options
Delta changes over time!
S changes
Time declines
Other factors (r, s) may change
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True Delta Hedging Adjust hedge when S changes
Scenarios 1 & 2:
IBM stock drops by $1 to $73.49 ==> Loss of $1000 Call options also drop by $0.5197 ==> Gain of $1037.97
==>Net change $37.97
IBM stock rises by $1 to $75.49 ==> Gain of $1000
Call options also rise by $0.5193 ==> Loss of $1037.97
==> Net change ($37.97)
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True Delta Hedging Adjust hedge when t changes
Scenario 3: One week passes, IBM stock at $71.49 ==> Loss of $3000 Call options now worth $2.73 ==> Gain of $3173
==>Net change $173
New call delta = 0.4029 New hedge ratio = 1/0.4029 = 2.482 ==> Sell 5 more contracts!
Scenario 4: One week passes, IBM stock at $77.49 ==> Gain of $3000
Call options now worth $5.82 ==> Loss of $2698==> Net change ($302) New call delta = 0.6238 New hedge ratio = 1/0.6238 = 1.603 ==> Buy 3 contracts!
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True Delta Hedging Adjust hedge when S changes
Scenarios 1 & 2:
IBM stock drops by $1 to $73.49 ==> Loss of $1000 Put options also rise by $0.4803 ==> Gain of $1008.63
==>Net change $8.63
IBM stock rises by $1 to $75.49 ==> Gain of $1000
Put options also fall by $0.4803 ==> Loss of $1008.63
==> Net change ($8.63)
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True Delta Hedging Adjust hedge when t changes
Scenario 3: One week passes, IBM stock at $71.49 ==> Loss of $3000 Put options now worth $6.06 ==> Gain of $2835
==>Net change ($165)
New put delta = 0.4028 1 = -0.5972 New hedge ratio = 1/0.5972 = 1.674 ==> Sell 4 contracts!
Scenario 4: One week passes, IBM stock at $77.49 ==> Gain of $3000
Put options now worth $3.15 ==> Loss of $3276==> Net change ($276) New put delta = 0.6238 1 = -0.3762 New hedge ratio = 1/0.3762 = 2.658 ==> Buy 5 more contracts!
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Delta Hedging with options
Delta represents response of call (or put) price withchange in the stock price
Delta changes as stock price, time to expiration,interest rates, volatility change
It is too expensive to hedge individual stock positionswith matching options. It is more common to hedge
a portfolio with index options (cross hedging)
Most managers monitor delta itself to decide when torebalance.
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A True Protective Put
Puts can be used to build a floor under the value of a longposition
Buy 1 put per long share
Ex.: Long 1000 shares of IBM at $74.49 Buy 1000 puts at $4.71
Puts guarantee a value of $75 per share
This is insurance, not a hedge!
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A True Protective Put
IBM Profit S Profit P Combined90 15,510 -4,710 10,80085 10,510 -4,710 5,80080 5,510 -4,710 80075 510 -4,710 -4,200
74.49 0 -4,200 -4,20070 -4,490 290 -4,20065 -9,490 5,290 -4,20060 -14,490 10,290 -4,20055 -19,490 15,290 -4,200
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Hedging with Futures (example from May 2001)
There are futures on the S&P500. Suppose I have a portfoliothat is currently worth $1,117,672. The portfolio has a beta of1.3.
June S&P500 futures are at 1430.70
==> contract is worth 500 x 1430.70 = $715,350 Hedge ratio =
(Value of portfolio / Value of Futures contract)(Portfolio Beta)
= (1,117,672/715,350)(1.3) = 2.031 ==> Sell 2 Contracts !
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Hedging with Futures (example from May 2001)
S&P Spot
in June
%
ch
an
ge Port. inJune%
cha
ngeProfit
Portf
olioProfit
Futur
es Combined1573.75 10% 1,262,969 13.0% 145,297 -143,050 $2,2471502.25 5% 1,190,321 6.5% 72,649 -71,550 1,099
1430.7 0% 1,117,672 0.0% 0 0 01359.15 -5% 1,045,023 -6.5% -72,649 71,550 -1,099
1287.65 -10% 972,375 -13.0%-
145,
297 143,050 -2,247
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Adjusting Systematic Risk with Futures
PM may choose to adjust systematic exposure up or down toreflect investor desires expectations of market movements
About index futures: Represents contract to make/take delivery of a portfolio
represented by the index Since index itself may be non-investable, most index futures
contracts are cash-settled example:
S&P500 futures CME contract value = 250 x index Initial margin: $6K for spec, $2.5K for hedgers.
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Adjusting Systematic Risk with Futures
I have an $11 million stock portfolio with b=1.05. I want toincrease b to 1.2.
Value of Futures = 1314.50 x 250 = $328,625
bf = 1.0. Target b = contribution from portfolio + contribution from
futures 1.2 = (1.0)(1.05) + [(F x 328,625)/$11,000,000](1.0) F = (bT - Wsbs)(Vs/VF)
F = 5.02 => buy 5 contracts What have we done? Used futures contracts to leverage holdings and increase
exposure to market risk
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Adjusting Systematic Risk with Futures
Suppose target b = .90
0.90 = (1.0)(1.05) + [(F x 328,625)/$11,000,000](1.0)
F = (.90 - 1.05)(33.4728)(1.0) = -5.02 contracts (sell)
We have shorted futures to reduce systematic exposure.
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Hedging with Interest Rate Futures
How do you reduce duration for a bond portfolio? Sell high D, buy low D Sell bonds, buy Tbills Sell interest rate futures
Interest rate futures: agreement to make/take delivery of afixed income asset on a particular date for an agreed upon price
ex: Sept Tbond futures contract $100K FV US Treas bonds with 15-years to maturity and 8%
coupon (what if they don't exist?)
Price: 99-27 = 99 27/32 % of $100,000 = $998,437.50 (Tick = $31.25) D = 8.64 years
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Hedging with Interest Rate Futures
I own an $11,000,000 face value portfolio of high grade UScorporate bonds with an aggregate value of 101-08 (or$11,137,500) and a duration of 7.7 years.
I expect rates to rise. How can I immunize my portfolio? Target D = contribution of bond port + contribution of fut.
0 = (1.0)(7.7) + [(F x 998,437.50)/11,137,500](8.64) F = (0.0 - (1.0)(7.7))(11,137,500/998,437.50)/8.64
F = -9.94 contracts => short 10 Tbond futures contracts
This is the weighted average duration approach
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