Use DerivaGem to calculate the value of an American put option on a non-dividend-paying stock when the stock price is USD $30, the strike price is USD $32, the risk-free rate is 5% p.a. continuously compounded, the volatility is 30% p.a. and the time to maturity is 1.5 years. (Choose Binomial American for the option type and 50 time steps.)

(a) Calculate the options intrinsic value. Calculate the options time value.

(b) What would a time value of zero indicate? What is the value of an option with zero time value?

(c) Using a trial and error approach, calculate how low the stock price would have to be for the time value of the option to be zero. (use 50 time steps)