Question

Consider a call option on a stock, the stock price is $23, the strike price is $20, the continuously risk-free interest rate is 9% per annum, the volatility is 39% per annum and the time to maturity is 0.5.

(i) What is the price of the option? (6 points).

(ii) What is the price of the option if it is a put? (6 points)

(iii) What is the price of the call option if a dividend of $2 is expected in 60 days? (8 points)

Answer 1

Answer>

t = 0.5

Considering a yearly option, time to expiry = 365*0.5 = 182.5

Using black-Scholes model for calculation of option premium,

Call Premium C = S*N(d1) - X*(e^(- r*t))*N(d2)

Put premium P = X*(e^(- r*t))*N(-d2) – S*N(-d1)

Where,

d1 = [Ln (S / X) + (r + (Dv^2) / 2) *t]/(Dv*(t^0.5))

d2 = d1 - Ds*(t^0.5)

Here,

C = price of a call option

P = price of a put option

S = price of the underlying asset

X = strike price of the option

r = rate of interest

t = time to expiration

Ds = volatility of the underlying

N represents a standard normal distribution with mean = 0 and standard deviation = 1

Using this values to calculate the price of the call option using the above formula in the option calculator,

we get C = 4.75 , P = 0.86

a> The value of call option premium is 4.75

b> The value of put option premium is 0.86

c> if the dividend $2 is expected in 60 days:

Dividend yield = annual divided / share price = 2 / 23 = 0.0869 = 8.69%

Hence value of call option = 4.00

I have used option calculator to derive these values.