Price a European Call & Put and an American Put on a stock that is currently selling at $25 and has a volatility of 20%. The options all have a life of 9 months and a strike price of $26. The risk-free rate for all horizons up to 9-months is 3% per annum with continuous compounding.

a. Use a 9-step binomial tree to price all 3 options

b. Use a 10-step binomial tree to price all 3 options

c. Use the Black-Scholes-Merton formula to price the European options

Now the stock will pay a dividend of $1 in 3 months from today. Price European Call & Put and American Call & Put using a 3-step binomial tree for each option.