## BSM - Kindly give a reply of this question..

pinalkaria87
Posts: 5
Joined: Thu Oct 04, 2012 11:12 pm

### BSM - Kindly give a reply of this question..

A three-month European call option on the S&P 500 index is purchased at-the-money (ATM) when the index is at 1,400. The volatility of the index is 30.0% per annum and the dividend yield is 2.0% per annum. The risk-free rate is 3.0%. Assume that N(d1) = N(0.0917) = 0.54 and N(d2) = N(-0.0583) = 0.48. Which is nearest to the price of the call?

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swarnendupathak
Finance Junkie
Posts: 119
Joined: Mon Sep 17, 2012 11:06 am

### Re: BSM - Kindly give a reply of this question..

Hi pinalkaria87,
You should use BSM formula to derive the call price, but So to be adjusted with the dividend yeild. The revised spot rate would be So*e^-(0.25*0.02)i.e.1400*e^-(0.25*0.02)= 1393.02. Then use the BSM call price formula i.e.
{So*N(d1)}-{X*e^-rt*N(d2)}.

Regards
Swarnendu

content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

### Re: BSM - Kindly give a reply of this question..

Thanks Swarnendu,

The method you provided is absolutely right.