Question

Mondi is currently selling for R50. In a year’s time, the price could increase by 10% or fall by 5%. The interest rate is 1% .Calculate the current price of a European call option on the stock with an exercise price of R48.

Answer 1

HIgh Price = 55

Low Price = 47.50

r = 0.01

t = 1

U = High Price / Current Price = 55 / 50 = 1.1

D = Low Price / Current Price = 47.50 / 50 = 0.95

Probability of U = e^r*t - D / U -D

= e^(0.01*1) - 0.95 / 1.1 - 0.95

= 0.40

Payoff at U = Max (High Price - Strike Price,0)

= Max (55 - 48, 0)

= 7

Payoff at D = Max (Lower - Strike Price,0)

= Max (47.50 - 48, 0)

= 0

Price of the call Option = e^(-r*t) * (probability of U * Payoff at U + (1- probability of U) * Payoff at D)

= e^(-0.01*1) * (0.40 * 7 + (1-0.40) 0)

= $2.77