Question

Consider a non-dividend paying stock currently priced at $100 per share. Over any given 6- month period, the stock price is expected to go up or down by 10%. The continuously compounded risk-free rate is 8% per annum. The stock’s real-world continuously compounded expected return is 16% per annum. a) (5%) Calculate the current price of a 1-year strike-100 European call option on the stock. b) (5%) Calculate the real-world continuously compounded expected return on the call

Answer 1

We first calculate the risk-neutral probability in the tree. We get

(b) The true probability of an up move is given by:

Expected return on stock = 16%

u = 0.1

d = -0.1

exp(0.16*0.5) = 1.08

With the true probability of an up move being

p = [{exp(0.16*0.5)-1} - (-0.1)] / [0.1-(-0.1)] = 0.92

Continuously compounded expected return on the call :

e^-2(0.5*γ) [0.922*21 + 2*0.92*(1-0.92)*0 + (1-0.92)2*0] = 9.61

where γ = Continuously compounded expected return on the call

e^-2(0.5*γ) * 17.637 = 9.61

γ = 0.6072