Question

Let S = $100, K = $120, σ = 30%, r = 0.08, and δ = 0. Compute the Black-Scholes call price for 1 year to maturity.

Answer #1

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 = | 1 | |||||

K = Strike price = | 120 | |||||

r = Risk free rate = | 8.0% | |||||

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

σ = Std dev = | 30% | |||||

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

d1 = (ln(100/120)+(0.08-0+0.3^2/2)*1)/(0.3*1^(1/2)) | ||||||

d1 = -0.191072 | ||||||

d2 = d1-σ*t^(1/2) | ||||||

d2 =-0.191072-0.3*1^(1/2) | ||||||

d2 = -0.491072 | ||||||

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

N(d1) =0.424235 | ||||||

N(d1) = Cumulative standard normal dist. of d2 | ||||||

N(d2) =0.311688 | ||||||

Value of call= 100*0.424235-0.311688*120*e^(-0.08*1) | ||||||

Value of call= 7.9 |

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Question 34
Black-Scholes
Option-Pricing
S
45
Current
stock price
X
50
Exercise
price
r
5.00%
Risk-free
rate of interest
T
9 months
Time to
maturity of option
Variance
6.308%
Stock
volatility
1.
Call option price =
4.63
2.
Call option price =
2.83
3.
Call option price =
2.93
4.
Call option price =
2.63
5.
None of Above

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