Question

Suppose a stock is currently trading at 92 and the annual risk free rate is 0.0018.

What is the price of a call option on this stock with an expiration date T = 0.5 (times in years) and with an exercise price K = 98. Assume the volatility of annual log return is sd = 0.2

What is the price of a put option on the same stock with the same parameters

Answer #1

As per Black Scholes Model | ||||||

Value of call option = (S)*N(d1)-N(d2)*K*e^(-r*t) | ||||||

Where | ||||||

S = Current price = | 92 | |||||

t = time to expiry = | 0.5 | |||||

K = Strike price = | 98 | |||||

r = Risk free rate = | 0.2% | |||||

q = Dividend Yield = | 0% | |||||

σ = Std dev = | 20% | |||||

d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2) | ||||||

d1 = (ln(92/98)+(0.0018-0+0.2^2/2)*0.5)/(0.2*0.5^(1/2)) | ||||||

d1 = -0.369668 | ||||||

d2 = d1-σ*t^(1/2) | ||||||

d2 =-0.369668-0.2*0.5^(1/2) | ||||||

d2 = -0.511089 | ||||||

N(d1) = Cumulative standard normal dist. of d1 | ||||||

N(d1) =0.355815 | ||||||

N(d2) = Cumulative standard normal dist. of d2 | ||||||

N(d2) =0.304644 | ||||||

Value of call= 92*0.355815-0.304644*98*e^(-0.0018*0.5) | ||||||

Value of call= 2.91 |

As per Black Scholes Model | ||||||

Value of put option = N(-d2)*K*e^(-r*t)-(S)*N(-d1) | ||||||

Where | ||||||

S = Current price = | 92 | |||||

t = time to expiry = | 0.5 | |||||

K = Strike price = | 98 | |||||

r = Risk free rate = | 0.2% | |||||

q = Dividend Yield = | 0% | |||||

σ = Std dev = | 20% | |||||

d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2) | ||||||

d1 = (ln(92/98)+(0.0018-0+0.2^2/2)*0.5)/(0.2*0.5^(1/2)) | ||||||

d1 = -0.369668 | ||||||

d2 = d1-σ*t^(1/2) | ||||||

d2 =-0.369668-0.2*0.5^(1/2) | ||||||

d2 = -0.511089 | ||||||

N(-d1) = Cumulative standard normal dist. of -d1 | ||||||

N(-d1) =0.644185 | ||||||

N(-d2) = Cumulative standard normal dist. of -d2 | ||||||

N(-d2) =0.695356 | ||||||

Value of put= 0.695356*98*e^(-0.0018*0.5)-92*0.644185 | ||||||

Value of put= 8.82 |

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