1. On 11/6/23 IBM is priced at $149 and you wish to value the 2/16/24 (102 days) K = $150 call option with = 21%. Over that period, r = 5.3% and a $1.66 dividend will be paid in 2 and 95 days. (a) (5 points) Compute a 15-step binomial tree using the Schroder method: First generate the price tree for the prepaid forwards then at each time step, add back the PV of the expected dividends to get the underlying stock price. (b) (4 points) Compute the price of the European and American call option prices. (c) (2 points) Since European options can be priced with the Black-Scholes model, what is the price of K = 150 call with 102 days to expiration? Use formula found on slide 12-10. (d) (2 points) What is the risk-neutral probability that you will pay the strike price using BlackScholes? Recall slide 12-4. (e) (3 points) Suppose IBM unexpectedly increases its quarterly dividends from 1.66 to 1.8, what are the respective European and American call option prices? Use Black-Scholes to price the European option. Note: You cannot use the BT model in R to solve this since it has not been implemented for stocks with discrete dividends! If you set this up in Excel, solving is much easier, especially changing assumptions for part (e)