Question

A stock price follows geometric Brownian motion with an expected return of $16 \%$ and a volatility of $35 \%$. The current price is $$\$ 38$$. (a) What is the probability that a European call option on the stock with an exercise price of $$\$ 40$$ and a maturity date in 6 months will be exercised? (b) What is the probability that a European put option on the stock with the same exercise price and maturity will be exercised?

   A stock price follows geometric Brownian motion with an expected return of $16 \%$ and a volatility of $35 \%$. The current price is $$\$ 38$$.
(a) What is the probability that a European call option on the stock with an exercise price of $$\$ 40$$ and a maturity date in 6 months will be exercised?
(b) What is the probability that a European put option on the stock with the same exercise price and maturity will be exercised?

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Options, Futures, and Other Derivatives

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 15, Problem 8

Instant Answer

Step 1

We convert this to a decimal by dividing by 100, so the drift rate is 0.16. The volatility rate is given as 35%. We convert this to a decimal by dividing by 100, so the volatility rate is 0.35. Show more…

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A stock price follows geometric Brownian motion with an expected return of $16 \%$ and a volatility of $35 \%$. The current price is $$\$ 38$$. (a) What is the probability that a European call option on the stock with an exercise price of $$\$ 40$$ and a maturity date in 6 months will be exercised? (b) What is the probability that a European put option on the stock with the same exercise price and maturity will be exercised?

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