Question

Find the current fair values of a D1 month European call and a D2 month European put option, using a current stock price of D3, strike price of D4, volatility of D5, interest rate of D6 percent per year, continuously, compounded. Obtain the current fair values of the following:

1.European call by simulation.

2.European put by simulation.

3.European call by Black-Scholes model.

4.European put by Black-Scholes model.

D1	D2	D3	D4	D5        D6
11.2	10.9	31.7	32.6	0.65      9.5

Answer 1

Soln : As per the given data , Stock Price ,D3 = 31.7,

Strike price, D4 = 32.6 , Volatility , D5 = 0.65 and interest rate D6 = 9.5% , time to maturity, t = 1 month = 1/12 years

3) Now as per Black scholes formula for call:

D1= call price = D3* N(d1) - D4*e^-D6*t *N(d2)

on solving we get d1 = -0.0132 and d2 = d1 - D5*t^0.5 = -0.2008

So N(d1) from normal distribution table , N(-0.0132) = 0.495 and N(d2) = N(-0.2008) = 0.42074

D1 = 31.7* 0.495 - 32.6 * e^-0.095/12 * 0.42074

on solving we get , D1 = 15.695 - 13.608 = 2.083

4) D2 = D4e^(-r*T)*N(-d2) - D3*N(-d1) = 32.6* e^-0.095/12 * N(0.2008) - 31.7 * N(0.0132)

D2 = 32.6* 0.99211 *0.57926 - 31.7*0.505 = $ 2.73

European put value using black scholes = 2.73