Question

A company current stock price at RM16.00, the exercise price at RM17.00. If government bond yield is 10%, and the company’s share prices volatile at 35% in annualised form. The company does not pay any dividend. Using the Black-Scholes option pricing model, calculate:

(i) the fair value for a RM17.00 call option with 90 days to maturity.
(ii) the fair value for a RM17.00 put option with 90 days to maturity.
(9 Marks in total)

Answer 1

(i)

As per Black sholes Model,

Value of call option =

S0 = current price

N = Cumulative standard nprmal distribution function

E = Exercise price

r= risk free rate

e = 2.7182818

t = time to maturity

= standard deviation or volatility.

Ln = natural Logarithm

hence,

Ln 16/17 = -0.0606246218

N (d1) = N(-0.120) =0.45224

N(d2) = N(-0.294)=0.38413.

Value of call option =

hence fair value of call option = $0.86

(ii)

As per Black sholes Model,

Value of put option =

N(-d2) = 1-N(d2) = 1-0.38413=0.61587

N(-d1) = 1-N(d1) = 1-0.45224=0.54776

hence,

Value of put option =

hence fair value of put option = $1.45