Question

1. Calculate the value of the D1 parameter for a call option in the Black-Scholes model, given the following information: Current stock price: $65.70 Option strike price: $74 Time to expiration: 7 months Continuously compounded annual risk-free rate: 3.79% Standard deviation of stock return: 22%

2. Calculate the value of the D2 parameter for a call option in the Black-Scholes model, given the following information: Current stock price: $126.77 Option strike price: $132 Time to expiration: 6 months Continuously compounded annual risk-free rate: 1.41%; Standard deviation of stock return: 25%

Answer #1

1

S = Current price = | 65.7 | ||

t = time to expiry = | 0.583333333 | ||

K = Strike price = | 74 | ||

r = Risk free rate = | 3.8% | ||

q = Dividend Yield = | 0% | ||

σ = Std dev = | 22% | ||

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

d1 = (ln(65.7/74)+(0.0379-0+0.22^2/2)*0.583333333333333)/(0.22*0.583333333333333^(1/2)) | |||

d1 = -0.492426 |

2

S = Current price = | 126.77 | ||

t = time to expiry = | 0.5 | ||

K = Strike price = | 132 | ||

r = Risk free rate = | 1.4% | ||

q = Dividend Yield = | 0% | ||

σ = Std dev = | 25% | ||

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

d1 = (ln(126.77/132)+(0.0141-0+0.25^2/2)*0.5)/(0.25*0.5^(1/2)) | |||

d1 = -0.100423 | |||

d2 = d1-σ*t^(1/2) | |||

d2 =-0.100423-0.25*0.5^(1/2) | |||

d2 = -0.2772 |

1. What is the
value of the following call option according to the Black Scholes
Option Pricing Model? What is the value of the put options?
Stock Price = $55.00
Strike Price = $50.00
Time to Expiration = 3 Months = 0.25 years.
Risk-Free Rate = 3.0%.
Stock Return Standard Deviation = 0.65.
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$ ??????
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Excel Online Structured Activity: Black-Scholes Model
Black-Scholes Model
Current price of underlying stock, P
$33.00
Strike price of the option, X
$40.00
Number of months unitl expiration
5
Formulas
Time until the option expires, t
#N/A
Risk-free rate, rRF
3.00%
Variance, σ2
0.25
d1 =
#N/A
N(d1) =
0.5000
d2 =
#N/A
N(d2) =
0.5000
VC =
#N/A

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C=S×e−dt×N(d1)−E×e−Rt×N(d2)C=S×e−dt×N(d1)−E×e−Rt×N(d2)
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