The three-month S&P 500 futures contract is trading at a level of 1250.The rate of interest is 2%.The average rate of dividends for stocks in the index is 3%.Index volatility is 20%.What is the Black-Scholes price of a one-year at-the-money put option on the futures?

Question

Quizplus · Accepted Answer

Use the formula given in Chapter 14.Note that dividends are irrelevant,as explained in the chapter.
> F=1250
> K=1250
> r=0.02
> d=0.03
> v=0.2
> T=1
> d1=(log(F/K)+(0.5*v^2)*T)/(v*sqrt(T))
> d2=d1-v*sqrt(T)
> put = exp(-r*T)*(K*pnorm(-d2)-F*pnorm(-d1))
> put
[1] 97.59798

The Three-Month S&P 500 Futures Contract Is Trading at a Level