1. Suppose the current stock price of stock XYZ is $80. The annualized expected stock return (c.c.) is 10% and the annual stock price volatility is 40%. The risk free interest rate is constant and 5% (c.c.).

(a) What is the price of a European call option with 9 months to maturity and a strike price of $100?

(b) What is the price of a European put option with 6 months to maturity and a strike price of $90?

(c) What is the price of the put option in b) if stock XYZ pays a dividend of $5 in 3 months?

(d) Construct a binomial tree with 2-time steps. i. What is the price of the European put option with 6 months to maturity and a strike price of $90 if stock XYZ does not pay any dividends? ii. What is the price of the European put option with 6 months to maturity and a strike price of $90 if stock XYZ pays a dividend of $5 in 3 months? iii. What is the price of the put option in ii) if it is American?