3. A non-dividend-paying stock is trading at So 100, and the interest rate is 6 ln(1.01). (a) Use a two-period binomial model with up and down factors u = 1.16, d = 0.91 and up probability p = 0.7 to price a European put option with strike K = 110 and maturity T in eight months. (b) Price an American put option with the same strike (and maturity). What is the probability that you will exercise early? (c) Suppose the stock has suddenly become 10% more volatile, and the company announced that it will pay a one-off cash dividend of $5 per share six months from now. Explain how this new development can be captured in the model above. Make appropriate adjustment to your model parameters, price the European and American put option in part (a) and part (b) using an 8 step binomial tree. Discuss the results. (d) Your colleague uses the Black-Scholes model to price the European put option and gets a different answer. How can you improve your model to try to match with theirs? Demonstrate in Excel how a closer match can be achieved. 3. A non-dividend-paying stock is trading at So 100, and the interest rate is 6 ln(1.01). (a) Use a two-period binomial model with up and down factors u = 1.16, d = 0.91 and up probability p = 0.7 to price a European put option with strike K = 110 and maturity T in eight months. (b) Price an American put option with the same strike (and maturity). What is the probability that you will exercise early? (c) Suppose the stock has suddenly become 10% more volatile, and the company announced that it will pay a one-off cash dividend of $5 per share six months from now. Explain how this new development can be captured in the model above. Make appropriate adjustment to your model parameters, price the European and American put option in part (a) and part (b) using an 8 step binomial tree. Discuss the results. (d) Your colleague uses the Black-Scholes model to price the European put option and gets a different answer. How can you improve your model to try to match with theirs? Demonstrate in Excel how a closer match can be achieved