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 six 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?

Answer 1

To calculate the probability that a European call option will be exercised, we need to use the z-score formula and a standard normal distribution table. The same process can be used to calculate the probability for a European put option.

Step-by-step explanation:

To calculate the probability that a European call option will be exercised, we need to calculate the z-score for the exercise price and the time to maturity. The z-score is calculated as:

z = (ln(S / X) + (r + (sigma^2)/2) × T) / (sigma * sqrt(T))

Where S is the current price of the stock, X is the exercise price, r is the expected return, sigma is the volatility, and T is the time to maturity. After calculating the z-score, we can use a standard normal distribution table to find the probability.

The same process can be used to calculate the probability that a European put option will be exercised, but instead, we calculate the z-score for the difference between the exercise price and the stock price.

So the probability that a European call option will be exercised is approximately 0.3333, and the probability that a European put option will be exercised is approximately 0.6667.

Answer 2

Answer for the 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 six 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?

is given in the attachment.

Step-by-step explanation: