Question

The valuation of a European call option on a stock that does not pay dividends is given by c = S*N(d1) - X*e(-rT)*N(d2) Given a strike price of 75, a spot price of 70, volatility of 25%, time to expiry of 0.33 years, a risk free rate of 8%, N(d1) = 0.411078 and N(d2) = 0.356293, what is the price of a call option?

*2.9317

*2.7498

*2.5412

*3.0241

Answer 1

Black Scholes model is used to calculate theoretical price of an option.

The formula to calculate price of call option is :

= S* N(d₁) - X*(e^-rt)*N(d₂)

Here S= Current Spot Price

X= Strike Price of Option

t= time remaining till expiration i.e. expressed as a percentage of year

r= continously compounded risk free rate

e= exponential function

Price of Call option:

= 70*0.411078 - (75/e^0.08*0.33)*0.356293

=28.77546 - (75/e^0.0264)*0.356293 ( here the value of e^0.0264 is 1.02675 ) we divide it, because we use negative sign in power i.e. e^-_^rt

This value i.e. e^-_^rt is given for calculation purpose, But as this value is not given

in excel the formula to derive this value is:

exp(0.0264)

=28.77546-(75/1.02675)*0.356293

=28.77546-(73.046*0.356293)

=28.77546-26.02578

=2.7497 approx