Question

Use the Black-Scholes formula for the following stock:

Time to expiration	6 months
Standard deviation	50% per year
Exercise price	$52
Stock price	$50
Annual interest rate	3%
Dividend	0

Calculate the value of a put option. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

1. Value of Put Option =

I NEED to see this worked out by hand (pen & paper) to understand and learn how to do it on my own without the use of excel. Please show all work in arriving at an answer. Thanks!

Answer 1

As per Black Scholes Model
Value of call option = S*N(d1)-N(d2)*K*e^(-r*t)
Where
S = Current price =		50
t = time to expiry =		0.5
K = Strike price =		52
r = Risk free rate =		3.0%
q = Dividend Yield =		0.0%
σ = Std dev =		50%
d1 = (ln(S/K)+(r-q+σ^2/2)*t)/(σ*t^(1/2)
d1 = (ln(50/52)+(0.03-0+0.5^2/2)*0.5)/(0.5*0.5^(1/2))
d1 = 0.10827
d2 = d1-σ*t^(1/2)
d2 =0.10827-0.5*0.5^(1/2)
d2 = -0.245283
N(d1) = Cumulative standard normal dist. of d1
N(d1) =0.543109
N(d1) = Cumulative standard normal dist. of d2
N(d2) =0.403119
Value of call= 50*0.543109-0.403119*52*e^(-0.03*0.5)
Value of call= 6.51
As per put call parity
Call price + PV of exercise price = Spot price + Put price
6.51+52/(1+0.03)^0.5=50+Put value
Put value = 7.75