A stock price is currently $30. During each two-month period for the next four months it is

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Question:

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?

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) How much is the value of the option, if it is an American option?

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) Use a one-step binomial tree to value this option.
3) 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-Scholes-
Merton formula.