Question

Use the Black-Scholes formula for the following stock: Time to expiration 6 months Standard deviation 54%...

Use the Black-Scholes formula for the following stock:

Time to expiration 6 months
Standard deviation 54% per year
Exercise price $54
Stock price $52
Annual interest rate 4%
Dividend 0

Calculate the value of a put option.

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Answer #1

d1=[ln(S/X) + (R – d + σ^2 / 2) × t] / (σ ×t^0.5) =Ln(52/54)+(4%-0%+54%^2/2)/(54%*0.5^0.5) =0.14445

N(d1) using NORMSDIST function of excel =NORMSDIST(0.14445) =0.5574

d2 =d1-σ*t^0.5 =0.5574-54%*0.5^0.5=-0.2374
N(d2) using NORMSDIST function of excel =NORMSDIST(-0.2374) =0.4062

Call Option =C = S * N(d1) – X × e–Rt × N(d2) =52*0.5574-54*EXP(-4%*0.5)*0.4062 =7.23

Put option=C0-S0+X*EXP-rt =7.23-52+54*EXP(-4%*0.5) =8.16

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