Question

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 = $37.63 Strike Price = $35.00 Time to Expiration = 3 Months = 0.25 years. Risk-Free Rate = 4.0%. Stock Return Standard Deviation = 0.65.

Answer 1

Following is the European call & put option formula to calculate the value of call option under the Black-Scholes Model where K is the strike price

C = S*N (d1) - N (d2) *K*e ^ (-r*t)                  

P = Ke^–rt * N(–d2) – SN(-d1)

Where

C = call value

P = Put value

S = current stock price

N = cumulative standard normal probability distribution

t = days until expiration

Standard deviation, SD = σ

K = option strike price

r = risk free interest rate

Formula to calculate d1 and d2 are -

d1 = {ln (S/K) +(r+ σ^2 /2)* t}/σ *√t

d2 = d1 – σ *√t

Lets calculate the values in excel -

INPUTS		Outputs	Value
Standard deviation (Annual) (σ)	65.00%	d1	0.4162
Time until Expiration (in Years) (t)	0.25	d2	0.0912
Risk free rates (Annual) (r)	4.00%	N(d1)	0.6614
Stock Price (S)	$37.63	N(d2)	0.5363
Strike price (K)	$35.00	B/S call value (C )	6.3024
Dividend yield	0%	B/S Put Value (P)	3.3241

Call value (C) is $6.3024

Put Value (P) is $3.3241

Formulas used in excel calculation: