Introduction to Financial Derivatives

Lecture #2 on option

Jinho Bae

May 1, 2008

Outline

1. Review

2. Margins of an option

3. Closing out an option position before expiration

4. Payoff of an option at an expiration date

1. Review• Gim-daeri buys a put option to sell a Samsung

share for \600,000 in three months.• He pays \10,000 of premium for the option• Suppose that the price of a Samsung share is \

550,000 at the expiration date.– He exercises the option, i.e., sells the share at \0.6M.– He earns \40,000 b/c he can buy a share for \0.56M

in the spot market.

• Return of this investment– Amount invested: \10,000– Profit: \40,000

%400100000,10

000,40Return

• Now suppose that the price of a Samsung share is \610,000 at the expiration date.– He does not exercise the option b/c he can

sell it for \610,000 in the spot market.– He earns nothing from this investment.

• Return of this investment– Amount invested: \10,000– Profit: \-10,000– Return: -10,000/10,000*100(%)=-100%

2. Margins

• Option holder – needs to pay the option price in full when purchasing

options– has no obligation to fulfill the terms of option contracts– is not required to maintain funds in a margin account

• Option writer– may not be able to fulfill the terms of option contracts if

the option is exercised– is required to maintain a margin account

• In general, no marking to market for options, unlike futures.

3. Closing out an option position before maturity

• An option position can be closed by issuing an offsetting order for the same option

• An example– On 5/1, Young-hee buys the right to buy a Samsung s

hare for \600,000 on 8/1 [Long call]. She pays \15,000 as a premium.

– On 5/2, she sells the right to buy a Samsung share for \600,000 on 8/1 [Short call]. She is paid \20,000 as a premium.

Is this an offsetting order?

– On 5/1, Young-hee buys the right to buy a Samsung share for \600,000 on 8/1.

– On 5/2, she sells the right to buy a Samsung share for \610,000 on 8/1.

– The answer is

– Young-hee’s position on 5/2• One long call on Samsung with strike price of 600,000• One short call on Samsung with strike price of 610,000

The effect of offsetting orders on open interest

① Case where the open interest goes down by one contract

– Both investors are offsetting existing positions– On 5/1, Young-hee buys the option and Chul-soo se

lls the option.– On 5/2, she sells the option and he buys the option.

The effect of offsetting orders on open interest

② Case where the open interest stays the same– One investor is offsetting an existing position but the

other is not– On 5/1, Young-hee buys the option and Chul-soo se

lls the option.– On 5/2, she sells the option and Gil-dong buys the o

ption. Gil-dong is a new investor.

4. Payoff of an option at expiration

• It is determined by the price of underlying asset at the expiration date

• Key features– Option holder faces an unlimited profit and a

limited loss– Option writer faces an unlimited loss and a

limited profit

1) Long callpayoff

0

S, Price of underlying asset at maturity

-c

X

X+c

45°

• when S<X, Not exercised payoff=-c

• when S>X, exercised payoff=S-(X+c)

2) Short callpayoff

0

c

X

X+c

45°

• when S<X, Not exercised payoff=c

• when S>X, exercised payoff=(X-S)+c

S, Price of underlying asset at maturity

3) Long putpayoff

0

-pX-p

X

payoff=-p

payoff=(X-S)-p

S, Price of underlying asset at maturity

• when S<X,

Not exercised• when S>X,

exercised

4) Short putpayoff

0

pX-p

X

• when S<X,

Not exercised payoff=p• when S>X,

exercised payoff=(S-X) +p

S, Price of underlying asset at maturity