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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