In: Finance
You are attempting to value a call option with an exercise price of $109 and one year to expiration. The underlying stock pays no dividends, its current price is $109, and you believe it has a 50% chance of increasing to $130 and a 50% chance of decreasing to $88. The risk-free rate of interest is 12%. Calculate the call option’s value using the two-state stock price model.
c0= | Call price | = | [∏c1+ + (1-∏)c1- ]/ (1+r) | |
p0= | Put price | = | [∏p1+ + (1-∏)p1- ]/ (1+r) | |
Where | ||||
∏= | Risk neutral probability | = | (1+r-d)/(u-d) | |
r= | risk free interest rate | = | 12.0000% | |
u= | up factor | = | 1.1927 | |
d= | Down factor | = | 0.8073 | |
∏= | Risk neutral probability | = | ||
= | 0.5000 | |||
1- ∏= | = | 0.5000 | ||
S0 = | Stock price today | = | 109 | |
S1+ = | = 109*1.1927 | = | 130 | |
S1- = | = 109*0.8073 | = | 88 | |
X = | Exercise price | = | 75 | |
c1+ = | = Max(0, S1+ - X) | |||
= Max(0, 130 - 75) | = | 55 | ||
c1- = | = Max(0, S1- - X) | |||
= Max(0, 88 - 75) | = | 13 | ||
c0= | (0.5*55 + 0.5*13) /(1+0.12 ) | = | 30.36 |
Answer is:
30.36