uppose that the stock of Stiawmot is currently trading at $60. Suppose also that it can only take two possible values in a year from now: It can either go up by 25% or down by 20%. The annual risk-free rate is 10%. Assume that the stock pays no dividend.

a. Draw the one-period tree for the evolution of the stock price and the one-period tree for lending $1

Suppose that we are interested in pricing a European put option on this stock. The option has a strike price of $66, and its maturity is exactly one year from now.

b. In order to price the option, we first form a replicating portfolio by buying shares of the stock and by lending B dollars at the risk-free rate. What is the cost of this portfolio as a function of and B?

c. Draw the one-period binomial tree for this portfolio.

d. What are the two equations that will have to be satisfied by and B?

e. Solve the equations for and B. In words, what is your portfolio?

f. Using your answer from part (e), what should the price of the put option be?

g. Since the stock price can only take two possible values at the end of the year in

this binomial world, you are not perfectly satisfied with this price. Calculate a more reasonable price for this put option using the Black-Scholes formula (and something else...!). In your calculations, use a stock price volatility ( ) of 0.22.