A non-dividend paying stock currently trades for $73.55 and has an annualised return standard deviation of 25.7%. Given that the continuously compounded risk-free rate of return is 2.65% p.a complete the following

1. Using a two-step binomial tree, price the European put option on the stock when the put has an exercise price of $75 and 6 months to maturity.
2. Using a two-step binomial tree, price the American put option on the stock when the put has an exercise price of $75 and 6 months to maturity.
3. Use BSM to calculate the theoretical price of the European put option.
4. Explain what you would do if you held a European option that you no longer want to be exposed to.