An investment manager expects a stock to be quite volatile and is considering the purchase of either a straddle or a chooser option. The stock is priced at 44, the exercise price is 40, the continuously compounded risk-free rate is 5.2 percent, and the volatility is 51 percent. The options expire in 194 days. The chooser option must be declared a call or a put exactly 90 days before expiration.
a. Determine the prices of the straddle and the chooser.
b. Suppose at 90 days before expiration, the stock is at 28. Find the value of the chooser option at expiration if the stock price ends up at 50 and at 30.
c. Suppose at 90 days before expiration, the stock is at 60. Find the value of the chooser option at expiration if the stock price ends up at 50 and at 30.
d. Compare your answers in c and d to the performance of the straddle.