Question

A stock price is currently S = 100. Over the next year, it is expected to go up by 100% (u = 2) or down by 50% (d = 0.50). The risk-free interest rate is r = 20% per annum with continuous compounding. What is the value of a 12-month European Put option with a strike price K = 100?

Answer 1

Standard inputs :

S = Stock price = 100

E = Exercise price = 100

u = 2

d= 0.5

uS = 100*2 = 200

dS = 100 *0.5 = 50

R = e^risk free rate = e^0.2 = 1.2214

Risk neutral probability = ( R - d) / ( u -d) = (1.2214 -0.5 ) / ( 2 - 0.5 ) = 0.4809

1 - p = 1 - 0.4809 = 0.5191

payoff from put option = Max [ Exercise price - stock price ,0 ]

payoff in upmove = 0 as the stock price is higehr than the exercise price

payoff in downmove = 100 - 50 = 50

Expected payoff = 0.409 *0 + 0.5191 * 50 = 25.95

Value of the call option = 25.95 / 1.2214 = 21.25