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 $24 at the end of one month. If the outcome is negative, it is expected to be $18 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.