Problem Set 3

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.

a) Value this option using a two-period binomial tree.

b) 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.

a) Value this option using the Black-Scholes formula. Illustrate each step in your

calculation.

b) Please use a one-step binomial tree to value this option.

c) Please use a two-step binomial tree to value this option.

d) Compare the results from b) to c) with what you get using the Black-ScholesMerton

formula.