A company is currently awaiting the outcome of a major lawsuit. This is expected to be known within 1 month. The stock price is currently $20. If the outcome is positive, the stock price is expected to be $24 at the end of 1 month. If the outcome is negative, it is expected to be $18 at this time. The 1-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 1-month call options with strike prices of $19, $20, $21, $22, and $23?

(c) Use DerivaGem to calculate a volatility smile for 1-month call options.

(d) Verify that the same volatility smile is obtained for 1-month put options.