Question

A European call option has 3 months to expiry and a strike price of $32. The underlying stock has a current price of $28 and volatility (σ) of 0.35 per annum. The riskfree rate of interest is 5% per annum.

The Black-Scholes price of this call option is $Answer.

The intrinsic value of this option is $Answer.

Enter an answer to 2 decimal places. Do not enter the dollar sign ($).

Answer 1

The formula for call option using Black Scholes model

C= S N(d1) - Xe^-rtN (d2)

S = current stock price = $28

X = exercise price or strike price = $32

σ = 0.35

t = 3 months = 3/12 = 0.25

r = risk free rate = 5%

d1 = [ln (S/X)) + (r + σ²/2) *t]/ σ * sqrt (t)

d2 = d1 - σ * sqrt(t)

ln = natural logarithm

d1 = [ln (28/32)) + (0.05+ 0.35²/2) *0.25]/ 0.30 * sqrt (0.25)

d1= (-0.13353 + 0.02781) /0.15 = -0.7048

d2 = d1 - s * sqrt(t) = -0.7048– 0.15 = -0.8548

N(d1) = NORMSDIST (-0.7048) = 0.2405 (where NORMSDIST is the excel function for cumulative probability density function)

N(d2) = NORMSDIST (-0.8548) = 0.1963

C= S N(d1) - Xe^-rtN (d2)

C= 28*0.2405 – 32 * e^-0.05*3/12 * 0.1963= 6.734 – 6.2035 = 0.5305

Call option= $0.53

Intrinsic value = Stock price – strike price = $28-$32 = -$4

As this value is negative, the intrinsic value = $0

Answers:

The Black-Scholes price of this call option is $0.53

The intrinsic value of this option is $0.