Question

Let S = $80, K = $70, r = 6% (continuously compounded), d = 2%, s = 40%, T = 1, and n = 2. In this situation, the appropriate values of u and d are 1.35370 and 0.76886, respectively. What is the value of p*, the risk-neutral probability of an upward movement in the stock price at any node of the binomial tree?

Option D is the correct answer, but how?

Answers:

a. 0.4882

b. 0.5097

c. 0.3533

d. 0.4298

e. 0.5702

Answer 1

This is the case of a dividend paying stock.

In the case of a dividend paying stock, the formula for risk neutral probability is as shown below:

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

where other variable are already defined and t = T / n = 1 / 2 = 0.5

hence, p* = [e^{(0.06 - 0.02) x 0.5} - 0.76886] / (1.3537 - 0.76886) = 0.429760858 = 0.4298

Hence, the correct answer is option d. 0.4298