A stock price has an expected return of 16% and volatility of 35%. The current p

Question

A stock price has an expected return of 16% and 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 maturity date in 6 months will be exercised?

B.) What is the probability that a Europena put option on the stock with the same exercise price and maturity will be exercised?

Breakdown and show in excel please

Explanation / Answer

Call would be exercised if stock price in 6 months is greater than the exercise price of 40. So, we have to find the probability of stock price in 6 months be more than 40. Let stock price in 6 months be St. ln(St) would follow a normal distribution with mean=ln(38)+(0.16-0.35^2/2)*(6/12)=3.687 and variance=0.35^2*(sqrt(6/12))^2=0.247^2..Required probability=P(ln(St)>ln(40))=1-N((ln(40)-3.687)/0.247)=1-N(0.008)=area to the right side of 0.008=1-NORMDIST(0.008,0,1,TRUE)=0.4968 Put would be exercised if stock price in 6 months is less than the exercise price of 40. So, we have to find the probability of stock price in 6 months be less than 40. This is equal to 1-probability of stock price in 6 months be more than 40=1-0.4968=0.5032

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