Question

A stock price is currently $60. It is known that over each of the next two three-month periods it will go up by 10% or down 8%. The risk-free interest rate is 11% per annum with continuous compounding. Use the risk-neutral approach to find the value of a six-month European put option with a strike price of $60?

Answer 1

To find the value of a six-month European put option with a strike price of $60 using the risk-neutral approach, calculate the expected future value of the stock price at expiration and compare it with the strike price.

Step-by-step explanation:

To find the value of a six-month European put option with a strike price of $60 using the risk-neutral approach, we need to calculate the expected future value of the stock price at expiration and compare it with the strike price.

Here are the steps:

1. Calculate the future stock price at expiration after each possible movement, considering a 10% increase and an 8% decrease.
2. Calculate the probability of each possible movement based on the given information.
3. Discount the future stock prices at expiration to their present values using the risk-free interest rate of 11% per annum with continuous compounding.
4. Calculate the expected future value of the stock price at expiration by summing the discounted future stock prices weighted by their probabilities.
5. Compare the expected future value with the strike price to determine the payoff of the put option.
6. Discount the payoff to the present value using the risk-free interest rate.

By following these steps, you can find the value of the six-month European put option with a strike price of $60 using the risk-neutral approach.