A company is currently awaiting the outcome of a major lawsuit. This is expected to be known within one month. The stock price is currently $20. If the outcome is positive, the stock price is expected to be S24 at the end of one month. If the outcome is negative, it is expected to be S18 at this time. The one-month risk-free interest rate is 8% per annum.

a. What is the risk-neutral probability of a positive outcome?

b. What are the values of one-month call options with strike prices of $19, $20, $21, $22, and $23?

c. Use DerivaGem to calculate a volatility smile for one-month call options.

d. Verify that the same volatility smile is obtained for one-month put options.