Question

Use the Black-Scholes model to find the value for a European put option that has an exercise price of $62.00 and four months to expiration. The underlying stock is selling for $63.50 currently and pays an annual dividend of $2.07. The standard deviation of the stock’s returns is 0.24 and risk-free interest rate is 5.5%. (Round intermediary calculations to 4 decimal places. Round your final answer to 2 decimal places.)

Answer 1

We can use following method to calculate the European put option for dividend paying stock under the Black-Scholes Model

P = Put value =?

S = current stock price = $63.50

N = cumulative standard normal probability distribution

t = days until expiration = 4 months or 4/12 = 0.33 years

Standard deviation, SD = σ = 0.24

K = option strike price = $62

r = risk free interest rate = 5.5% per year

Dividend yield q = annual dividend/ current stock price = $2.07/$63.50 = 3.26%

Formula to calculate d1 and d2 are -

d1 = {ln (S/K) +(r-q + σ^2 /2)* t}/σ *√t

d2 = d1 – σ *√t

INPUTS		Outputs	Value
Standard deviation or Volatility (Annual) (σ)	0.24	d1	0.296
Time until Expiration (in Years) (t)	0.33	d2	0.157
Risk free rate (Annual) (r)	5.50%	N(d1)	0.6163
Current Market Price (S)	$63.50	N(d2)	0.5624
Strike price (K)	$62.00	B/S call value (C )	$4.47
Dividend yield	3.26%	B/S Put Value (P)	$2.53

Price of Put option is $2.53

Formulas used in excel calculation: