Question

The stock price is currently $110. Over each of the next two six-month periods, it is expected to go up by 12% or down by 12%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100?

Answer 1

  

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HIgh Price = 123.2

Low Price = 96.8

r = 0.08

t = 1

U = High Price / Current Price = 123.2 / 110 = 1.12

D = Low Price / Current Price = 96.8 / 110 = 0.88

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

= e^(0.08*1) - 0.88 / 1.12 - 0.88

= 0.8470

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

= Max (123.2 - 100, 0)

= 23.2

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

= Max (96.8 - 100, 0)

= 0

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

= e^(-0.08* 1) * (0.8470 * 23.2 + (1-0.8470) *0)

= $18.139605453 OR 18.14