Question

A stock price is currently $40. It is known that at the end of 1 month it will be either $42 or $38. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a 1-month European call option with a strike price of $39?

Answer 1

Upmove (U)= High price/current price=42/40=1.05

Down move (D)= Low price/current price=38/40=0.95

Risk neutral probability for up move

q = (e^(risk free rate*time)-D)/(U-D)

=(e^(0.08*0.08333)-0.95)/(1.05-0.95)=0.56689

Call option payoff at high price (payoff H)

=Max(High price-strike price,0)

=Max(42-39,0)

=Max(3,0)

=3

Call option payoff at low price (Payoff L)

=Max(Low price-strike price,0)

=Max(38-39,0)

=Max(-1,0)

=0

Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L)

=e^(-0.08*0.08333)*(0.566887*3+(1-0.566887)*0)

=1.69