Question

a stock index currently stands at 300 and has a volatility of 20% per year. the continuously compounded risk-free interest rate is 3% per year and the dividend yield on the index is 8%. a trader used a two-step binomial tree to value a six-month american call option on the index. what is the risk-neutral probability that the stock price moves up in 3 months?

Answer 1

Solution:

Given that dividend yield, d = 0.08, Risk-free interest rate, r = 0.03, Time, t = 3/12, Stock price, S = 300, volatility = 20%

Since the volatility is 20%, the given up factor, u = 1.20 and the down factor, d = 0.80

The risk neutral probability is

p* = [e^(r - d)t - d]/(u - d)

p* = [e^(0.03 - 0.08) (3/12) - 0.80]/(1.20 - 0.80)

p* = (0.98758 - 0.80)/0.40

p* = 0.4689

Hence, the  risk-neutral probability that the stock price moves up in 3 months is p*^2 = (0.4689)^2 = 0.2199.