The Option Contract (BKM 20.1)

Investment and Portfolio

Management

(FIN3IPM)

Semester 2, 2007 Lecture 11 Option Markets

10-2

Student Notices

zThe subject guide states that sections 20.1 to 20.5 from BKM are to be covered in week 12.

zWe will in fact cover only sections 20.1 – 20.4, inclusive from BKM.

zSection 20.5 will not be covered in class and is not examinable.

10-3

The Option Contract (BKM 20.1)

zCall Option – the right to purchase an asset at a specified price (exercise or strike) on or before a specified date.

zIn order to obtain this right, you pay for the option – the price of the option is called the premium. zTwo parties involved, the option purchaser and the

seller of the option (option writer).

zRefer to example: March 2003 calls on Microsoft, exercise of $22.50. Available on March 4 2003 for $1.15.

zCurrent stock price = $23.07.

10-4

The Option Contract

z Does buying a call option make any sense in this case.

z If you pay $1.15 now, you have the right to buy a Microsoft share from the option writer for $22.50 on or before the end of March. (third Friday of month) z Buy and hope share price rises.

z If share price is $23.50 at end of March, exercise for an option payoff of $23.50 - $22.50 = $1.

z Your profit is payoff less option price = $1 $1.15 = -$0.15.

z You exercise to reduce your loss from $1.15 to $0.15.

10-5

The Option Contract

zPut Option – the right to sell an asset at a specified price (exercise or strike) on or before a specified date.

zAgain, pay for this right – the price of the put option is also called the premium.

zAgain, two parties involved, the option purchaser and the seller of the option (option writer). zRefer to example: March 2003 puts on Microsoft,

exercise of $22.50. Available on March 4 2003 for $0.55.

zCurrent stock price = $23.07.

10-6

The Option Contract

zDoes buying a put option make any sense in this case.

zIf you pay $0.55 now, you have the right to sell a Microsoft share to the option writer for $22.50 on or before the end of March. (third Friday again)

zThe value of the call is presently $22.50– 23.07=-$0.57

zWhy pay $0.55 –hope that share price will fall.

10-7

The Option Contract

zVarious terms exist to describe options.

zAn option is out of the money if it has a negative payoff to immediate exercise – the IBM call option was out of the money.

zOption is in the money if immediate exercise provides a positive payoff – the IBM put was in the money.

zAn option is at the money if the share price is equal to the strike or exercise price.

zOptions are traded on a standardised basis – expiry dates, assets and exercise prices

10-8

The Option Contract

z Can be traded over the counter – non standard contracts – not very common.

z American – option type that can be exercised at any point in time up to and including expiry.

z European – option type that can be exercised only at expiry.

z Assets on which options exist include – Shares, Indices, Futures contracts, Foreign Currency and interest rates.

z Used for risk management purposes.

10-9

Option Values at Expiry (BKM 20.2)

zThe key to valuation at expiry is the exercise price. zValue can be split into two parts.

zFor a call option, at expiry, if share price is above exercise price, option is worth share price minus exercise.

zIf share price is below exercise price, option is worthless – cheaper to buy share on market.

⎩ ⎨ ⎧

≤ > −

=

X S

X S X S

T T T

if 0

if holder

call to Payoff

10-10

Option Values at Expiry

z Use the previous equation to reproduce the table valuing a call option in page 706.

z The value of the option goes up $ for $ when price is above X.

z Can draw a diagram Fig 20.3:

$

ST X

Payoff

Profit Premium

10-11

Option Values at Expiry

zThe diagram shows that the exercise price is where the kink is.

zPayoffs to call option writer are the same but negative. (mirror image in horizontal axis) zWhat the option holder makes, the option writer

loses.

zSee Figure 20.4 in BKM.

zPut option value at expiry is also linked to the exercise price.

zFor put option, if price is above exercise, the put is

worthless – sell in market. 10-12

Option Values at Expiry

z

If share price is below exercise price, value of

put at expiry is exercise less share price.

z

Unlike the call, there is a limit on the profit

from a put.

z

If share price falls to zero, put is worth X.

Can draw a payoff diagram to put holder, as

in Figure 20.5.

⎩ ⎨ ⎧

< −

≥ =

X S S X

X S

T T

T if

10-13

Option Values at Expiry

z Put writer has payoffs and profits which are identical and opposite to put holder.

z Naked put writing – written put without cash or some other means by which the position is offset – can lead to large losses.

z Similarly – Naked call writing.

$

ST X

Payoff

Profit Premium

10-14

Option Values at Expiry

z Options versus stock investments – options are an alternative means to get exposure to shares. z Consider three

strategies-– A – buy 100 IBM shares

– B – buy 1000 options on IBM shares($10), X=$100. – C – buy 100 calls for $1000. Invest rest in T-bills(3%). z Table summarises the results – A is just 100 times

share price – B is option value, 0 if less than $100, share price-$100 if greater than $100.

z Case C is FV of 9000 @ 3% + value of 100 options.

10-15

Option Values at Expiry

IBM Stock Price

$95 $100 $105 $115

All Stock $9,500 $10,000 $10,500 $11,500

All Options $0 $0 $5,000 $15,000

Lev Equity $9,270 $9,270 $9,770 $10,770

10-16

Option Values at Expiry

z On the basis of a $10000 investment, we can calculate HPR’s as on page 709.

z Clearly strategy B has a much wider spread of returns – this entails more risk – easy to double money (relative to share investment) but also easy to lose 100%.

z Strategy C is called leveraged equity – limited downside of –7.3%, unlimited upside a little worse than shares only but have risked a lot less capital. z Options are giving a big return because of leverage –

allow access to shares at a fraction of cost. z See Figure 20.6, BKM for a summary.

10-17

Option Values at Expiry

IBM Stock Price

$95 $105 $115

All Stock -5.0% 5.0% 15%

All Options -100% -50% 50%

Lev Equity -7.3% -2.3% 7.7%

10-18

Option Strategies (BKM 20.3)

z Option strategy is a very large topic, limited by imagination.

z Five very common strategies are covered in Section 20.3.

z Protective put strategy – buy a share – what if it falls in value – buy a put so you can sell it at the strike price and limit your losses.

z Buy share only – worst possible outcome is lose the lot.

z Protective put – worst possible outcome is X-S-P.

10-19

Option Strategies

zIf share price rises, put is worthless, you make profit which is reduced by put premium – price paid to reduce risk.

zCovered Calls – you write or sell call options over stock which you own.

zThis is referred to as a buy and write strategy. zIf you have a long term strategy of buy and hold, can

be used to generate extra cash flow from assets. zLimits the upside – if share price rises above exercise

price, must sells shares and miss out on further upside.

10-20

Option Strategies

z With a covered call, if share price is below X, the option holder will not exercise – you get the premium and keep the shares.

z If share price is above X, shares are called at X – you must sell at exercise price – loss equals share price less exercise price + option premium.

z These strategies can be summarised in payoff diagrams – share payoffs are simply straight lines. z Study Straddle, Spread and collar in own time. z Option strategies are often discussed in financial

review in Smart Investor section of FinReview on Wednesdays.

10-21

Put – Call Parity (BKM 20.4)

zProtective put limits downside and unlimited upside.

zCan be replicated by bonds plus call. zIf price rises you profit.

zIf price falls, you have a guaranteed minimum return.

zPut call parity is all about the link between put and call option prices and being able to create these two positions at different prices – arbitrage.

10-22

Put – Call Parity

z You buy a share for S0and a put option with a strike price of X for $P.

z If share price is below X, you exercise put and collect X.

z If share price is above X, you collect S_T. z This is a protective put strategy which costs

S₀+P.

z Consider the following alternative – you buy a riskless zero coupon bond with a face value of X.

10-23

Put – Call Parity

zYou also buy a call option on the same stock (as the protective put) with an exercise price of X. This costs $C.

zIf the share price is below X, the call is worthless and your zero matures giving you $X.

zIf share price is above X, your zero matures, giving you $X, enough to exercise the option and collect ST. zThe payoffs to the protective put and zero plus call

strategies are identical.

zIn an efficient market, the cost of these two strategies must be equal.

10-24

Put – Call Parity

z The protective put costs: z The Call plus zero costs:

z We expect these to be equal in an efficient market:

z The point of all this is if we observe put and call prices and a risk free rate, we can check if the puts or calls are correctly valued.

P S0+

(

)

f

r X C

+ +

1

(

)

r X

C _T

f + = +

+ 0

10-25

Put – Call Parity

zIn other words, what we are looking for is an arbitrage opportunity.

zExample: Suppose we observe stock @$110, call with X=$105 @$17 and put with X=$105 @ $5 and a risk free rate of 10.25% pa.

zWhat is a protective put going to cost?

zWhat is the zero plus call going to cost?

115 $ 5 $ 110 $

0+P= + =

S

(

)

(

)

105 17

$

1+ = + + 0.5=

+ _T

f

r X C

10-26

Put – Call Parity

z We can buy the same thing two different ways – one is cheaper.

z What to do? Arbitrage opportunity! z Buy the cheaper one and sell the more

expensive one.

z Create the protective put position for $115. z Write the call, get $17, and borrow the PV of

$105 = $100 for 6 months.

z Use the money from the written call plus borrowings (=$117) to pay for the protective put.

10-27

Put – Call Parity

zWe end up with $2 left over – arbitrage profit. zThe point is that we have taken no risk. zThe long position is the protective put. zThe short position is the zero + call.

zWhatever the first does, the second will also do (in reverse) – since we are long in one and short in the other, we cannot lose money once positions are established.

zWe have not considered dividends – this will change things slightly – the cost of the protective put is reduced by the payment of dividends.

10-28

Put – Call Parity

z

We end up with a put call parity relationship

given by:

z

These arguments apply only to European

options.

z

If you write an American option, you could be

called or put early and the bond will not give

you sufficient funds to close out position –

you may lose your arbitrage profit.

( )

( )

S C

P= − 0+ +

10-29

zOption terminology – the range of special terms that apply to options.

zWhat we mean by a call and put option.

zUnderstand the payoffs to options – the importance of exercise price and how to draw a payoff diagram.

zKnow about the common option strategies.

zPut call parity – sets up a relationship between put and call (Euro) option values.