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FINA 471 Liang Ma Problem Set 4 Due on Wednesday, Dec 3rd, 12pm at my office (456D DMSB) Each group should submit one hard copy of the solution. The names (both the first and last names) of each student in the group should be written clearly on the first page of the hard copy. Clarity will be rewarded and disorganization will be penalized. Show your detailed work! 1. Binomial tree A stock price is currently $30. During each two-month period for the next four months it is expected to increase by 8% or decrease by 10%. No dividend payment is expected during these two periods. The risk-free interest rate is 5% per annum. Use a two-step tree to calculate the value of a European-style derivative that pays off [max(30-ST,0)]2, where ST is the stock price in four months? (hint: please note that this is not a typical put option, since the final payoff is the square of the normal put option payoff.) 2. Binomial tree Consider a six-month European put option on one stock. Suppose that the current stock price is 15, the strike price is 18.5, the continuously compounded risk-free rate is 2% per annum, and the volatility of the stock is 10% per annum. 1) Value this option using a two-period binomial tree. 2) Will the value of the option be different if it is an American option? 3. Black-Scholes-Merton and binomial tree Consider a six-month European call option on a non-dividend-paying stock. The stock price is $30, the strike price is $29, and the continuously compounded risk-free interest rate is 6% per annum. The volatility of the stock is 20% per annum. 1) Value this option using the Black-Scholes formula. Illustrate each step in your calculation. 2) Please use a one-step binomial tree to value this option. 3) Please use a two-step binomial tree to value this option. 4) Compare the results from 2) to 3) with what you get using the Black-ScholesMerton formula