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What is the value of a European call option if the underlying stock price is $ 100 , the strike price is $ 90 , the underlying stock volatility is 40 % and the risk - free rate is 4 % ? Assume t option has 60 days to expiration
What is the value of a European call option if the underlying stock price is $ 100 , the strike price is $ 90 , the underlying stock volatility is 40 % and the risk - free rate is 4 % ? Assume t option has 60 days to expiration
Expert Solution
| As per Black Scholes Model | |||
| Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t) | |||
| Where | |||
| S = Current price = | 100 | ||
| t = time to expiry = | 0.16667 | ||
| K = Strike price = | 90 | ||
| r = Risk free rate = | 4.0% | ||
| q = Dividend Yield = | 0% | ||
| σ = Std dev = | 40% | ||
| d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2) | |||
| d1 = (ln(100/90)+(0.04-0+0.4^2/2)*0.16667)/(0.4*0.16667^(1/2)) | |||
| d1 = 0.767668 | |||
| d2 = d1-σ*t^(1/2) | |||
| d2 =0.767668-0.4*0.16667^(1/2) | |||
| d2 = 0.604367 | |||
| N(d1) = Cumulative standard normal dist. of d1 | |||
| N(d1) =0.778658 | |||
| N(d2) = Cumulative standard normal dist. of d2 | |||
| N(d2) =0.7272 | |||
| Value of call= 100*0.778658-0.7272*90*e^(-0.04*0.16667) | |||
| Value of call= 12.85 |
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