Question 1) Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. a) What is the price of the option if it is a European call? b) What is the price of the option if it is an American call? c) What is the price of the option if it is a European put? d) Verify that put-call parity holds.

Question 2) The current price of a non-dividend-paying biotech stock is $140 with a volatility of 25%. The risk-free rate is 4%. For a three-month time step: a) What is the percentage up movement? b) What is the percentage down movement? c) What is the probability of an up movement in a risk-neutral world? d) What is the probability of a down movement in a risk-neutral world? Use a two-step tree to value a six-month European call option and a six-month European put option. In both cases the strike price is $150.