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Presentation or individual slides must not to be reproduced without the permission of Dr Helen Bendall
Option markets
Investments
Lecture 10
Topic 11
Dr Helen B Bendall
Dr Helen Bendall
What we covered in topic 10 Although financial analysts are interested in economic
earnings streams, found that often only accounting data are
readily available, so need to seek as much information as
possible from sources available
The balance sheet, income statement and cash flow
statements were reviewed along with key financial ratios -
liquidity, leverage, asset management, profitability – in order
to gain an insight into the performance of the firm and
managers of the firm.
The Du Pont method of decomposing the ROE allowed
separation of ROE into five ratios so as to isolate which
factors were driving performance
EVA or residual income, measures the dollar value of the
firm‟s return in excess of its opportunity cost. Firms with
positive EVAs are adding value to the firm and vice versa.Options markets 2
Dr Helen Bendall
Objectives
To learn basic principles of option valuation and how
securities can behave or be “tailored”to be like options
Be familiar with different types of options and option
characteristics
Be able to establish the pay-offs to option holders and
option writers resulting from various option trading
strategies.
Know what is meant by the put-call parity relationship
Identify “option-like” securities, understand how
financial engineering can create securities with
predetermined pay-offs and consider some “exotic”
options Options markets3
Dr Helen Bendall
Option terminologyAn option is the right but not the obligation to buy or
sell an asset or income stream for a specified price
(exercise or strike price) before or at a given maturity
date (exercise date)
Call option is the right but not the obligation to buy an
asset at a specified price on or before the exercise
date.
Put option is the right but not the obligation to sell an
asset at a specified price on or before the exercise
date
The holder of the option is the buyer and the writer of
the option is called the grantor or writer
The grantor of the option must fulfil obligation to buy/sell.Options markets
4
Dr Helen Bendall
Option terminology continued
American option can be exercised anytime up to
the exercise date.
Most options traded in the US are American options
with the exception of some foreign currency options
European option can only be exercised on the
pre-determined exercise date.
Premium is the price of the option and is the
“reward” to the grantor for accepting the risk that
the option may be exercised.
When buying an option we can say we are long
When selling an option we can say we are short. Options markets 5
Dr Helen Bendall
Options markets
6
Example If the buyer of a Westpac $16 call option with a 28
December 2011 expiration „exercises‟ the option,
the holder of the option has the right to purchase a
Westpac share from the option seller for $16
anytime before the expiry date
This is an American style option as can buy before
expiry date
When the buyer originally bought the call option, the
buyer paid a premium to the seller – the price of the
option, granting the right, but not the obligation, to
buy the share at the strike or exercise price of $16
The option seller, the grantor, is obliged to sell the
Westpac share for $16, if exercised
Profit = exercise price – cost of the option (premium)
Dr Helen Bendall
Options markets 7
Trading and stock options
OTC (over-the-counter), and ETO, (exchange
traded options) are traded by investors
Equity and index traded on ASX
Additional shares are not issued by the company
Options issued by firms are a way to raise
additional equity capital
Sometimes offered with each share in an IPO or
rights issue
Stock options offered to employees, if exercised
Increases number of shares on issue and dilutes
shareholding of existing equity holders
Dr Helen Bendall
Stock options – stock split adjustment
Option‟s contract must be adjusted to account for a
stock split.
The exercise price needs to be adjusted by a factor of
the split
The number of options held increased by the same
factor
Eg if there was a 2:1 split, option number would be
doubled with each option worth half of the original strike
price
If a dividend >10%, the number of shares covered by
each option is increased in proportion to the stock
dividend
The exercise price is reduced by that proportion.Options markets 8
Dr Helen Bendall
Options markets 9
Components
ASX-traded equity options are standardised
The underlying asset
The option price is derived, in part, on the price of the underlying asset. Also called a derivative security.
Expiry date
All unexercised options expire on this date
Exercise, or strike price
The price at which the call option can be bought
The price at which the put option can be sold
Contract size
One option contract on ASX gives exposure to 1,000 shares
Dr Helen Bendall
Options markets 10
Uses of options
Options are used in different ways
Risk management
Speculation
Diversification
To earn income
Leverage
Options exist on many other financial assets
Interest rates, indices, currencies, commodities,
options on other derivatives etc
Dr Helen Bendall
Options markets11
Why trade options?Can be traded on own or in conjunction with stock
If you think the price of a share will increase
Buy a call option
Eg If share price is above the strike price for the call
Exercise the option to buy the share at the exercise price
and sell it on the market for a profit
If you think the price of the share will fall
Buy a put option
Eg If the share price is below the strike price for the put
Exercise the option to sell the share at the exercise price
Options give greater leverage than equity
Dr Helen Bendall
Options markets 12
Call option valuation
A call option gives the right to BUY
The intrinsic value at any time is the value above
the exercise price that occurs if the option were to
be exercised
However, a call option would not be exercised if
the share price was less than the exercise price
So the intrinsic value would never be negative
The minimum intrinsic value is zero
Dr Helen Bendall
Options markets 13
Intrinsic value of a call option with a
strike price of $10
450
Intrinsic Value
Share Price$15
$5
$5 $10
Strike price
Dr Helen Bendall
Options markets 14
Intrinsic value of a call option
where
C is the intrinsic value of a call option
ST is the price of the share
X is the exercise price
The call option is in-the-money if ST > X
Profit to call holder = payoff – purchase price
max[0, ST – X] – c where c = cost of call (premium)
XSif
XSifXSC
T
TT
0Pay- off to holder of call
premium
paid for
option
Dr Helen Bendall
Options markets 15
Call option profit diagramstrike price $10 and premium $1.30
Share price
$-1.30
0
Profit
breakeven $15
$3.70
$10premium
Profit = [ST – X] – c
ST@$15 = [$15 – 10] – $1.30
= $3.70
X
strike price
Dr Helen Bendall
Intrinsic value (payoff) and profit of call
option at expiration (call holder)
XSif
XSifXSC
T
TT
0
Payoff for call option
= pay-off - premium
Breakeven =$114
Stock price $90 $100 $110 $120 $130
Option value 0 0 $10 $20 $30
16Options markets
Call holder’s profit
= payoff – premium
=max[0, ST – X] – c
Dr Helen Bendall
Payoff to call writer
0 if ST < X
- (ST - X) if ST >X
Profit to call writer
Payoff + premium
[ -(ST – X)] + c
Payoffs and profits at expiration
for call grantor
17Options markets
Breakeven = $114
X =
Examples
ST@112 = - (112-100) + 14
= -12 +14
= + 2
ST@116 = - (116-100) + 14
= - 16 +14
= - 2
Dr Helen Bendall
Options markets 18
“Moneyness” for call holder
A call option is in-the-money
If the share price is greater than the exercise price
i.e. ST > X
The option is out-of-the-money
If share price is less than the strike price
i.e. ST < X
The option is at-the-money
If share price is equal to the exercise price
ie ST = X
Dr Helen Bendall
Profits for call holder and writer at
expiration
Options markets
19
Share price
profits
+
-
strike price
breakeven
premium,c
sell call
buy call
Profits for put holder and grantor “mirror image”
x
Dr Helen Bendall
Options markets 20
Put option
A put option gives the right to SELL
If the share price is above the exercise price
Do not exercise
If market price below strike at expiry then exercise
1. Buy the underlying and
2. Make the put seller buy underlying asset from
you at the higher exercise price
3. Profit = intrinsic value pay-off – option premium
Dr Helen Bendall
Options markets 21
Put option intrinsic value pay-off
and profit to holder
where
P is the put option intrinsic value
ST is the share price
X is the exercise or strike price
Profit = max [0, X - ST] – p where p = put option premium
A put option is out-of-the-money if ST > X
would not be exercised
XSifSX
XSifP
TT
T0
Dr Helen Bendall
Options markets 22
Intrinsic value for a put option with a strike price of $25
$25 Share price
450
Intrinsic Value
$17
$8
$30
strike price
ST > X
ST < X
ST = X
To calculate profit subtract cost of option
Profit = [0,X – ST] - p where p = put premium
Dr Helen Bendall
Payoff and profit to put option holder
strike = $100
23Options markets
XSifSX
XSifP
TT
T0
Pay-offs for put holder
Profit for put holder
Profit = [X – ST] - p
breakeven Profit = [0] - p
p = put option premium
Dr Helen Bendall
Options markets 24
Put option holder‟s profit example strike price $15 and premium $0.80
$15 Share price
$-0.80
0
Profit
$9.20
$5 $14.20
$14.20
breakeven
premium, p
Profit = [X – ST] – p
@ $5 = $ [15 - 5] - 0.80
= $10 - 0.80
= $9.20
strike price
x
Dr Helen Bendall
Options markets 25
“Moneyness” for put holder
A call option is in-the-money
If the share price is less than the exercise price
i.e. ST < X
The option is out-of-the-money
If share price is greater than the strike price
i.e. ST > X
The option is at-the-money
If share price is equal to the exercise price
ie ST = X
Dr Helen Bendall
Profits: put option holder and writer
Options markets
26
Share price
profits
+
-
strike price
breakeven
Premium, p
sell put
buy put
Profits for put holder and grantor mirror image each other
If ST < X profits for put holder = (X - ST) - p
profits for put grantor= - (X - ST) + p
if ST > X option would not be exercised
if ST= X profit for holder = - p and profit for grantor = + p
Profits for holder = max[0,X - ST] - p
Profits for grantor = [0, - (X - ST)] + p
x
Dr Helen Bendall
Investment Strategy Amount Investment
Equity only Buy stock @ $100 100 shares $10,000
Options only Buy calls @ $10 1000 options $10,000
Options + Buy calls @ $10 100 options $1,000
Bills Buy T-bills @ 3% 1 T-Bill $9,000
Equity, options & leveraged equity
Exercise price, X, for option = $100
Assumption: The firm is not paying a dividend until after the
6 month period.
T-Bills at maturity = $9,000 x 1.03 = $9,270
Three strategies for a $10,000 investment for 6 months
27
Options markets
Dr Helen Bendall
Investment strategy pay-offs
Options markets
28
Portfolio Stock price
$95 $100 $105 $110 $115 $120
All stock $9,500 $10,000 $10,500 $11,000 $11,500 $12,000
All options 0 0 $5000 $10,000 $15,000 $20,000
Calls + T-Bills $9,270 $9,270 $9,770 $10,270 $10,770 $11,270
All stock portfolio = number of shares x share price
All options portfolio = 0 unless share price > strike
price when it becomes worth 1000 times the difference
between the stock price and exercise price = $100
Calls + T-Bill portfolio = face value of the Bill + pay-off
options
Call + T-Bill less risky as protects downside risk but pay-offs
less – an insurance strategy
Exercise price = $100
Dr Helen Bendall
Investment strategies rates of return
Options markets
29
Portfolio Stock price
$95 $100 $105 $110 $115 $120
All stock -5% 0% 5% 10% 15% 20%
All options -100% -100% -50% 0% 50% 100%
Calls + T-Bills -7.3% -7.3% -2.3% 2.7% 7.7% 12.7%
An option offers leverage. Calls are a leveraged investment on
stock
An increase of 4.3% in price of the share rate of return100%
A leveraged stock portfolio values respond more than
proportionally to changes in stock price ( 65%)
4.3% stock price rise
100% gain
Dr Helen Bendall
Rate of return to three strategies
Slope of all-option portfolio
steeper
Leveraged portfolio is far
more sensitive to the value of
the underlying security.
Call + T-Bill portfolio
demonstrates an insurance
strategy as downside risk
limited.
30
Options markets
Dr Helen Bendall
Value of a protective put
strategy
A protective put – the purchase
of stock combined with a put
option that guarantees minimum
pay-off = put‟s exercise price
Profit = pay-off – put premium, p
31
Options markets
Dr Helen Bendall
Protective put versus stock investment
Strategies (at-the-money option)
If ST=S0, profit on stock = 0 if stock
price unchanged
Profit on stock rises and falls by the
$1 for every $ swing in stock price
If ST>S0, profit on protective put
increases with increase in stock price
If ST<S0, profit on protective put is
negative = cost of put, P.
Protective put offers some
insurance against stock price declines
in that it limits losses a form of
portfolio insurance.Put-call parity = C + X = S0 + P
(1 + rf)T
S0 = ST at time 0
32Options markets
Dr Helen Bendall
Value of a covered call
Covered call strategy is a
combination selling a call option
together with simultaneously
buying the stock
Writing (granting) a call without
holding the stock is called a
naked call
Covered call grantors gain
additional premium but forego
capital gain when ST >X33
Options markets
Dr Helen Bendall
Straddle - buying put and call with same exercise
price – a long straddle.
Strips – two puts + one call with same maturity
Straps - two calls + one put with same maturity
Spreads - A combination of two or more call options
or put options on the same asset with differing
exercise prices or times to expiration.
Vertical or money spread:
same maturity date
different exercise price
Horizontal or time spread:
different maturity dates but same exercise price
Collars – limits value between upper and lower bounds
Other option strategies
34Options markets
Dr Helen Bendall
Value of a straddle
35
Options markets
Long straddle – buying call and put
on same strike price and maturity date
Useful strategy if believe the stock has
high volatility but not sure of direction.
Gain must be > cost of premiums
A worst case scenario is no movement
of stock – pay two premiums
Grantor of straddle would believe
stock had low volatility – gain premiums
but hope stock price does not move
much until expiration
Dr Helen Bendall
Value of a bullish spread (holder)
36
Options markets
Spread: combination of two or more calls
or puts on the same stock with differing
exercise prices or times to maturity
Money spread: sale and purchase with
differing exercise prices, same maturity date
Time spread: sale and purchase with
differing maturity dates – (not shown here)
Example is a money or vertical spread
Bullish spread holder‟s payoff either
increases or is unaffected by price increases
Holders of bullish spread benefit from
rising stock prices
Dr Helen Bendall
Put-call parity
Put-call parity theorem is an equation representing
the relationship between put and call prices.
Theorem developed by combining a call with
riskless bond so that a call + bond portfolio = stock
+ put portfolio
C + X = S0 + P
(1 + rf)T
With dividends put-call parity equals
P = C - S0 + PV(X) + PV(dividends)
Violation of the put-call parity allows arbitrage
opportunitiesOptions markets
37
Dr Helen Bendall
Stock price = $110 Call price = $17(1 yr expiration)
Put price = $5 (1 yr) Risk free = 5%
Maturity = 1 yr Strike price X = $105
C + X = S0 + P
(1 + rf)T
17 + 105/1.05 = 110 + 5
but 117 > 115 arbitrage
Since the leveraged equity (S0 + P) is less
expensive, acquire the lower cost alternative (right
hand side) and sell the higher cost (left hand side)
alternative. This would continue until parity
Put-call parity - disequilibrium example
38Options markets
Dr Helen Bendall
Arbitrage strategy
Exploiting arbitrage strategy
Buy the stock
Buy the put
Write a call and
Borrow $100 for one year (borrowing money is the
opposite of buying a bond)
C + X = S0 + P
(1 + rf)T
39Options markets
right hand side
left
hand
side
$2 inflow without any
offsetting outflows in yr 1
Dr Helen Bendall
Option-like securitiesCallable bonds = straight bond + call option
Conveys a call option to the issuer
Exercise price is the set bond repurchase price
Convertible securities = straight bond + call option
Conveys a call option to the holder
Most issued deep out of the money - so likely not to be exercised
Warrants are call options issued by the firm “stock options”
But an exercised warrant requires firm to issue a share
Unlike a call will result in cash flow to the firm
Collateralised loans
Conveys an implicit call or put option to the borrower
If a call, borrower hands over collateral with option of
reclaiming it back. 40
Options markets
Dr Helen Bendall
Value of callable bonds v straight
bonds
41Options markets
Callable bond = straight bond
+ call option to the issuer ie
investor is granting a call
Attached call means
investors must be
compensated for issuers right
to call in bond higher coupon
If issued at the same price
then the callable bond would
sell at a lower price ie bond
price minus cost of call.
Therefore must issue at
coupon rates > straight bond
Callable bonds potential for
capital gains are limited by the
firm‟s option to repurchase at
the call price
“Call in” bond if PV of scheduled
pmts + PV of FV > price of the bond
(in-the-money).
Dr Helen Bendall
Convertible bonds
Convertible bond is a bond with an option to
exchange the bond for a specified number of
shares.
Conversion ratio sets number of shares
Market conversion price is the current value of
shares for which the bond may be exchanged
A convertible bond must sell for more than its
straight bond value as it has more value
ie straight bond + call option
The value of straight debt is a function of stock price
of the issuing firm
Generally issued deep “out of-the-money” Options markets
42
Dr Helen Bendall
Value of a convertible bond v straight
bond
When stock prices are low, the
straight bond value is lower bound and
conversion is nearly irrelevant.
Convertible will trade like straight debt.
Convertible bond is a bond
with an option to exchange the
bond for a specified number of shares.
Investors convert if PV (bond
scheduled pmts + FV) < value of shares
The value of straight debt is a function
of the stock price of issuing firm
In strong firms debt is independent of
value of stock as default is low
In weak firms default increases and
straight bond value falls
When stock prices are high, the bond‟s
price is determined by its conversion
value
43
Options markets
Dr Helen Bendall
Convertible bond example
Bond A Bond B
Coupon pa $80 $80
Maturity date 10 yrs 10 yrs
Quality rating Baa Baa
Conversion ratio 20 30
Stock price $30 $50
Conversion value $600 $1250
Yield 10 yr Baa bonds 8.5% $8.5%
Value as straight debt $967 $967
Actual bond price $972 $1255
Reported YTM 8.42% 4.76%
Options markets 44
Bond A (close to straight debt)
Premium over straight bond = $5
$5 reflects low probability of conversion
YTM@ 8.42% close to straight debt @8.5%
Bond B is “in-the money” (close to equity)
Premium over straight bond (debt) = $288
Bond price reflects its conversion to equity
$5 difference between conversion value & PB
$5 reflects protection against stock price fall
YTM @4.76% < YTM debt @8.5%
Yield sacrifice indicates far greater value of
conversion option.
When stock prices are high,
PB is determined by its conversion
value. With conversion guaranteed
the bond is essentially equity.
Dr Helen Bendall
Convertible bond in practice
In theory value of convertible bond = straight debt
+ call option – but more difficult in practice.
Conversion price may increase in time
change in exercise price of option
Stocks may pay dividends over the life of the bond
so complicates valuation.
Most convertibles are also “callable” at the
discretion of the firm, so both parties holding
options.
When issuers use a call option knowing bond
holders will chose to convert, the issuer is said to
have forced a conversion.Options markets 45
Dr Helen Bendall
Warrants
Warrants are call options issued by the firm
Differ from call options as an exercised warrant
requires firm to issue a share, diluting value of
share of existing shareholder
Unlike a call, exercised warrants will result in cash
flow to the firm
Differences mean that warrant values will not be the
same as calls with same maturity date
Protected by adjustments against stock splits and
dividends
Often bonds are issued with a “sweetener” which
may be detached “detachable warrant” and sold
separately Options markets46
Dr Helen Bendall
Collaterised loan
Collateral provides an asset backing (the
borrower‟s guarantee) that the loan can be repaid.
Can be viewed either as an implicit call or put option
reflects put-call parity relationship
S0 – C = [L / (1 + rf)T] - P
Lender guaranteed that can sell asset if borrower
defaults on both right and left side but option gives
borrower the ability to chose whether to exercise or notOptions markets
47
Borrower hands over
collateral, $S, with call
option, $C, to repurchase
collateral asset when loan
repaid
Borrower is obligated to
pay $L but retains a put
option to sell asset to
lender (worth $P)
L = strike price
Dr Helen Bendall
Collateralised loan
Collateral is the borrower‟s
guarantee the loan will be repaid.
S0 – C = L/(1 + rf)T – P
The value of payment to be
received by the lender is the
minimum of ST, or L (strike price)
Can be expressed as ST – payoff
on a call (implicitly written by the
lender and held by the borrower)
Can be expressed as the receipt
of $L – proceeds of put option
Left hand side
right hand side
S0 – C = L/(1 + rf)T – P
Options markets
Dr Helen Bendall
Levered equity and risky debt
If a firm has borrowed and declared bankruptcy it is
an admission that funds are insufficient to pay claims
against it, the firm may discharge its obligations by
transferring ownership of assets to creditors.
Similar to collateralised loans, the required payment to
creditors represents the exercise price of the implicit
option, with the value of the firm the underlying asset.
Equity holders have a put option to transfer their ownership
claims to the creditors in return for the face value of the debt.
An alternate approach is that equity holders have a call
option – can claim back asset, if can pay off loan
Required pmt to creditors = strike price of implicit option
In corporate bond valuation, default premiums can be
calculated using option pricing techniques Options markets 49
Dr Helen Bendall
Return on index-linked CDs
Financial engineering can be used in the
creation of portfolios with specified pay-off
patterns
eg Options can be used to custom design
new securities such as index-linked CDs,
enabling investors to take a small position in
index options
The CDs will pay investors a specified
fraction of the rate of return on the market
index, while guaranteeing a minimum return,
should the market fall.
The CD is thus a call option – if the market
rises, the investor benefits according to
participation rate or multiplier- ie the slope,
but is “insured” against loss.
Participation rate (multiplier) calculation exampleIf rf = 6%, 6-mth at-the-money call on market index = $50, the index = 1000.
The option cost = C/S0= $50/1000 = $0.05 per $ of market value. The CD rate is
3% for 6mths. The breakeven multiplier = [ rf / (1 +rf) ] / [C /S0] = [0.03 /1.03] / [0.05]
= 0.0291/0.05 = 0.5825 where rf / (1 +rf) = PV of interest on each $ invested. 50
Options markets
Slope in this case = 0.58
ie buy 0.58 calls for every
$ invested
With slope = 0.7, investor
receives 70% of any CD
market increase
Dr Helen Bendall
Exotic options Asian options.
pay-offs depend on average price of the underlying asset
during its life or 0
Barrier options
Pay-offs depend on if underlying has crossed “a barrier” eg
“down-and-out” or “knockout options” expire worthless if stock
price crosses a set price or 0
Lookback options
Pay-offs depend on max price over life instead of at expiration
Currency options
asset price or exercise price denominated in foreign currency.
Eg quantos fix in advance exchange rate
Digital, binary, bet option
Pay-offs depend on a specified condition being met or 0
may pay a fixed amount if stock price > exercise price 51
Dr Helen Bendall
Summary
Understand what is an option and the terminology
and characteristics of different types of options
Established the pay-offs to option holders and option
writers (grantors) resulting from various option trading
strategies.
Learned what is meant by the put-call parity
relationship
Identified “option-like” securities which have implicit
embedded options – callable bonds, warrants etc
Saw how financial engineering can lead to creation of
portfolios with specified pay-offs
Considered a number of exotic optionsOptions markets 52