When a company commits (implicitly or explicitly) to granting at-the-money options to employees in the future then we can view them as a forward start options.

a) Explain the difference between a forward start option and a chooser option.

b) Describe carefully how the chooser options work and what the payoff of a simple chooser option is at the time, t₁, when some choice is made.

Explain what the variable T₂, t₁, and X represents in the formula given during classes for a chooser option.

c) Calculate the value of a simple chooser option with a time to expiration of 7 months and time to choose between a put or call equal to three months. The underlying stock price is 54, the strike is 54, the risk free interest rate is 8.3% (CONT) per annum, and the volatility per annum is 27%.

d) Use the put-call parity for vanilla European option to show that a chooser option is a package consisting a call option (specify the strike price and the maturity) and put options (specify the number of puts, strike price and maturity).

e) Use the result in bullet point d) to prove the formula given during classes.