Hi,

Can someone help me solve these homework questions? Please use a spreadsheet and show me step-by-step solution. Please see the attached file for the questions.

Thank you

One- Period Binomial Option Pricing: Suppose some stock currently selling for $80 will either increase in value over the next year to $100, or decrease in value to $64. The risk free rate over the period is 10% given annual compounding. [Let r denote the continuously compounded rate per year. Thus e rx1 = 1:1.] A call option on the stock with an exercise price of $75 matures in one period (1 year). (a) What are u and d? (b) What are the payoffs from the call in each state of the world? (c) What position in the underlying stock and bonds would allow you to replicate the payoff from the call? What is the cost of this replicating portfolio? What is the call price at time 0? Multi- Period Binomial Option Pricing: = 30% per year, erx1 = 1:05 per year, T = 4 Consider an American call.S0 = 40, X = 45, months = 1/3 year. The stock will pay no dividends over the four month life of the option. The changes in the stock's price can be approximated by a series of up and down movements and let there be 5 such movements over the 4 month life of the option; i.e., divide the four months into 5 periods. Let n = 5. The length of each interval is then T=n = (1/3)/5 = 1/15 year. Now we need 1 1 T a u and a d: the best place to get them is from . Let u=e n =e 15 , and d = u . [ 2 (a) Assuming a totally flat riskless term structure, what is the gross return on a riskless security over each of the intervals of length 1/15 of a year? (b) For each possible stock price and remaining time to maturity (i.e., at each node in the tree of stock prices), calculate and B (i.e., the components of the replicating portfolio) and the value of the call. c) Suppose the stock first declines in value and then increases during each of the remaining four periods. Use a table to show at each node the value of your stock and bond portfolio both before and after any trading in stock and borrowing/repayment of debt. Show explicitly how your stock purchases are financed by additional borrowing and how the proceeds of any stock sales are used to repay borrowing. Valuation and Replication of Puts: A stock is now selling for $100. Each month it will either increase or decrease in value by 10% (u = 1:1, d = 0:9). The riskless rate with annual compounding is 12:682503% per year. Note that 1:12682503 = 1:0112. A European put option on this stock with an exercise price of $105 matures in three months (n = 3). (a) Draw the tree of values for the stock price. (b) For each stock price and time to maturity (i.e., at all nodes of the tree), determine the value of the European put. (c) Assume that the put option is American (exercise price $105 and maturity in three months). Determine the value of this put for each stock price and time to maturity. When (at which tree nodes) would it be optimal to exercise this put option