Question

case study
Mr. Randa wants to earn by writing call option on hardy corporation stock . the current price of the stock is 1460 and Badal wants to write a 6 months call option with the striking price of 1500 dollars . Badal wants to determine the apropriate premium to charge for the call option . the stocks stanard deviation is 0.4 and the riskless rate of interist is asumed to be 10% . determine the premium value and recomend your decision

Answer 1

Using the Black Scholes Model, Value of call option is given by

C=S *N(d1)-K*e^(-r*t) * N(d2)

where d1= ( ln(S/K) + (r + s^2/2) *t ) / (s*t^0.5)

and d2 = ( ln(S/K) + (r- s^2/2) *t ) / (s*t^0.5) = d1- s*t^0.5

and S= spot price = 1460

K = strike price = 1500

r =risk free rate = 10% =0.1

s= standard deviation= 0.4

t= time till maturity in years = 6 months = 0.5 years

and N(d1) is the cumulative normal probabilty function upto d1

So, d1 = (ln(1460/1500)+(0.1+0.4^2/2)*0.5)/(0.4*0.5^0.5) = 0.222637

So, N(d1) = 0.5880911 (Can be obtained through NORMSDIST(0.222637) in excel)

d2 = 0.222637 - 0.4*0.5^0.5 = -0.0602054

So, N(d2) =0.4759960

Thus value of call option is given by

C= 1460*0.5880911 - 1500*e^(-0.1*0.5)*0.4759960

=179.44

The premium value os 179.44 . It is however, risky to write a call option on a stock , particularly a naked call when one does not possess the stock.

So, the advise is not to write the call option