- Options: General Properties 149
Exercise 7.1
Find the stock price on the exercise date for a European put option
with strike price $36 and exercise date in three months to produce a
profit of $3 if the option is bought for $4.50, financed by a loan at 12%
compounded continuously.The gain of an option buyer (writer) is the payoff modified by the premium
CEorPEpaid (received) for the option. At timeTthe gain of the buyer of a
European call is (S(T)−X)+−CEerT, where the time value of the premium is
taken into account. For the buyer of a European put the gain is (X−S(T))+−
PEerT. These gains are illustrated in Figure 7.1. For the writer of an option
the gains areCEerT−(S(T)−X)+for a call andPEerT−(X−S(T))+for a
put option. Note that the potential loss for a buyer of a call or put is always
limited to the premium paid. For a writer of an option the loss can be much
higher, even unbounded in the case of a call option.
Figure 7.1 Payoffs (solid lines) and gains (broken lines) for a buyer of Euro-
pean calls and puts
Exercise 7.2
Find the expected gain (or loss) for a holder of a European call option
with strike price $90 to be exercised in 6 months if the stock price on
the exercise date may turn out to be $87, $92 or $97 with probability^13
each, given that the option is bought for $8,financed by a loan at 9%
compounded continuously.