Question

A stock index is currently 1 ,500. Its volatility is 18%. The risk-free rate is 4% per annum (continuously compounded) for all maturities and the dividend yield on the index is 2.5% Calculate values for u, d, and p when a 6-month time step is used. What is the value a 12-month American put option with a strike price of 1,480 given by a two-step binomial tree.

Answer 1

u = e^(0.18*0.5^(1/2)) = 1.1357

d = 1/u = 1/1.1357 = 0.8805

p = [e^(0.04-0.025)*0.5 - 0.8805]/[1.1357-0.8805] = 0.4977

The tree is shown below in the attached image. The option is exercised at the lower node at the six month point. The worth is 78.41

a BbCc. 1934.84 0.00 1703.60 0.00 1500.00 78.41 1500.00 0.00 1320.73 159.27 1162.89 317.11 L0-J0 AM