Problem 5 Consider pricing options on a non-dividend-paying stock. We use the binomial lattice technique to price options. The current price of the stock is $150. The strike price is $160 and the option maturity is one year. The risk-free interest rate is 4% per annum (compounded continuously). We shall take the length of each time step of the lattice At equal to 3 months. Also, we assume that over each time step the stock price goes up by 15% or down by 15%. (a) Calculate the European call option price. (b) Calculate the European put option price. (c) Calculate the American call and put option prices. The delta of a stock option is the option price sensitivity to the underlying stock price change, which is the ratio of the change in the price of the stock option to the change in the price of the underlying stock. (d) Compute the deltas of the European call and put options at the end of the first time step. Hint: At the end of the first time step we have two nodes corresponding to the two possibilities. Therefore, we can use these two nodes to calculate the price differences at the end of the first time step. (e) Compute the deltas of the European call and put options at the end of the second time step. Note that you have to compute two deltas at the end of the second time step for each option