You are attempting to value a call option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it has a 50% chance of increasing to $124 and a 50% chance of decreasing to $76. The risk-free rate of interest is 8%. Calculate the call option's value using the two-state stock price model.
High price=Current price*up move=100*1.2667=126.67 | ||||||
Low price=Current price*down move=100*0.8933=89.33 | ||||||
Risk neutral probability for up move | ||||||
q = (e^(risk free rate*time)-D)/(U-D) | ||||||
=(e^(0.08*1)-0.8933)/(1.2667-0.8933)=0.5 | ||||||
Call option payoff at high price (payoff H) | ||||||
=Max(High price-strike price,0) | ||||||
=Max(124-100,0) | ||||||
=Max(24,0) | ||||||
=24 | ||||||
Call option payoff at low price (Payoff L) | ||||||
=Max(Low price-strike price,0) | ||||||
=Max(76-100,0) | ||||||
=Max(-24,0) | ||||||
=0 | ||||||
Price of call option = e^(-r*t)*(q*Payoff H+(1-q)*Payoff L) | ||||||
=e^(-0.08*1)*(0.5*24+(1-0.5)*0) | ||||||
=11.08 |
You are attempting to value a call option with an exercise price of $100 and one...
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