Question

Consider a futures contract on a non-dividend paying stock with futures price $20 and time to expiration 4 months. Assume that in four months the stock price will be either $22 or $19. Calculate the risk-neutral probabilities for the future stock prices.

Answer 1

Strike Price (K) = $ 20

Expected Price in 4 Months

S(upward) = $ 22

S(downward) = $ 19

Fair Future Price = $20

Let the Probability of attaining Upward price at the time of Expiry = "P"

Then,

($ 22 * P) + ($ 19 * (1 - P)) = $ 20

$ 22 P -$ 19 P = $ 20- $19

$3 P = $ 1

P = $ 1 / $ 3

Probability of Share price increases (P) = 0.3333

P(Upward) = 0.3333 (0r) 33.33%

Therefore P(Downward) = 1- 0.3333

P(Downward) = 0.6667 (or) 66.67%