Question

Assume that the riskless rate of interest is 4.5% and that the stock price has a volatility of 30%. Given a current stock price of $100 and the fact that the stock does not pay any dividend: a) What is the probability that a European put option on the stock with an exercise price of $90 and a maturity date in one year will be exercised? Hint: You need to compute the probability that the stock price at maturity will be less than or equal to $90. b) What is the probability that a European call option on the stock with an exercise price of $110 and a maturity date in one year will be exercised?

Answer 1

Part (a)

The required probability is 1 - N(d2) in the usual notation of Black Scholes Model.

Please see the table below:

100 9 30% 10 90 4.5% Risk free rate, R 12 Formula Used Values Output 13 0.651201719 (LN(C8/C11)+(C12+C10A2/2) C9)/(C10 SQRT(C9)) d1 14 0.351201719 C14-C10 SQRT(C9) d2 15 0.74254186 NORMSDIST(C14) N(d1) 16 0.63728149 NORMSDIST (C15) Nd2E 17

Hence, the probability that put option will be exercised = 1 - N(d2) = 1 - 0.63728149 = 0.36271851 = 36.27%

Part (b)

Probability that call option will be exercised = N(d2) = 0.63728149 = 63.73%