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?
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 |
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