Equity Derivatives

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Hi David,

I appreciate your support in making us understand risk managent.
Please guide me for understading of calculation of the price index in below question:

"Suppose the price for a six month S&P index future contracts is 552.3. If the risk free interest rate is
7.5% per year and the dividend yield on the stock index is 4.2% per year, and the market is
complete and there is no arbitrage, what is the price of the index today?"
(This question is from Philippe Jorian-Sixth edition)
Can you please explain solution in detail ( Specifically how the value T is calculated)
Best Regards,
Divya












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[David Harper CFA FRM]

Hi Dave,

The key formula is cost of carry for a commodity that pays a dividend:
F(0) = S(0)*exp((r-q)T)
... note that risk free rate (r) and storage (u) are (+) as costs of ownership while dividend (q) and convenience (y) are subtracts as benefits of ownership

but here we are solving for the spot:
F(0)/exp((r-q)T) = S(0) = F(0) * exp-((r-q)T) = 552.3*exp(-(7.5$-4.2%)*0.5) = 543.2618

Then just to test:
543.2618 spot *exp((7.5%-4.2%)*0.5) = 552.3 forward, confirms we are correct.

hope this helps, I can't find the Q&A in jorion's 6th (i don't see in chapter 7). If you'd point it out, i'd like to see what answer they give

Thanks, David

 

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Hi David,

Thanks for your excellent support and for quick response. Your answer is correct.

Thanks, Divya