Question

Return to Problem 35. Value the call option using the risk-neutral shortcut described in the box on page 533. Confirm that your answer matches the value you get using the two-state approach.

Question: You are attempting to value a call option with an exercise price of \(100 and one year to expiration. The underlying stock pays no dividends, its current price is \)100, and you believe it has a 50% chance of increasing to \(120 and a 50% chance of decreasing to \)80.

The risk-free rate of interest is 10%. Calculate the call option’s value using the two-state stock price model.

Short answer

Matches

Step-by-step solution

Given information

r_f = 0.1 (given)

u = 1.2

d = .8

Calculation of risk neutral probability that stock price will increase

P = 1 + r_f– d / u – d

= 1 + .1 - .8 / 1.2 - .8

= .75

Calculation of expected cash flow at expiration

E(CF) = .75 x $20 + .25 x 0 = $15

C = E(CF) / 1 + r_f

= $15 / 1.1

=$13.64

This value matches with the value found in problem 35.