Question

In question 3 above, what, to the nearest cent, is the value of a American put option with a strike price of $32 that expires in four months? (Your answer should be in the unit of dollar, but without the dollar sign. For example, if your answer is $1.02, just enter 1.02.)

Question 3:

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. If you use a two-step tree to do the valuation, what, to the nearest cent, is the value of a European put option with a strike price of $32 that expires in four months?

Answer 1

Solution to Question 3 -:

4 possible outcomes can be -:

1. Increase Increase = 30* (1.08)*(1.08)= 34.992

2. Increase Decrease = 30 * (1.08)*(.9) = 29.16

3. Decrease Increase = 30* ( .9)* (1.08) = 29.16

4. Decrease Decrease = 30* ( .9)* (.9) = 24.3

Only in option a the option would be exercised since the strike price is 32.

Now as per binomial tree formula for options -:

34.99*d- 2.99 + 29.16*d = 29.16*d + 24.3 *d

therefore, d= .28

Present Value = 34.99*.28* e^(-5%*2)

= 8.86

34.99*.28 - Call option price = Present Value

Call option price = .9372