Question

Question 34

1. Black-Scholes Option-Pricing
   S	45	Current stock price
   X	50	Exercise price
   r	5.00%	Risk-free rate of interest
   T	9 months	Time to maturity of option
   Variance	6.308%	Stock volatility

   	1.	Call option price = 4.63
   	2.	Call option price = 2.83
   	3.	Call option price = 2.93
   	4.	Call option price = 2.63
   	5.	None of Above

Answer 1

Black Scholes Option Pricing formula:

We take the value of sigma as the square root of variance, i.e. 25.12%

We start by finding the value of d1:

d1 =( ln(45/50) + (0.05+(0.2512^2)/2)*0.75) / (0.2512*sqrt(0.75))

d1 = (-0.105 + (0.05+0.0473)) / 0.2175

d1 = -0.2032

Finding d2:

d2 = d1 - 0.2512* sqrt(0.75)

d2 = -0.2032-0.2175

d2 = -0.421

Value of call option:

c = 45* N(-0.2032) - 50* exp(-0.05*0.75)*N(-0.421)

c = 45*0.4195 - 50* exp(-0.0375)*0.337 [to find the values of N(d1) and N(d2), please use excel and the function norm.s.dist(d1,true) and norm.s.dist(d2,true) ]

c = 2.64$

As this is closest to the 4th option, the answer is 4. Call option price 2.63