## Derivatives- Value of equity index forward formula

nivethasridhar3
Posts: 5
Joined: Wed Apr 13, 2016 6:39 am

### Derivatives- Value of equity index forward formula

Equity index forwards are continuously compounded.

We know that FP=S*(e^r*t) for continuous compounding.
Adjusting for benefits and cost of holding the underlying asset,

FP=S*e^(t*(r-q+c))
where q is rate of benefit- say dividend yield
c is rate of cost of holding
both continuously compounded.

If value at any point during the forward contract is Current spot price - PV(FP) - PV(benefits)

then Value (long) = S - FP*[e^(qt)/e^(rt)] ------>eq(1)

How does the value become S / e^(qt) - FP/ e^(rt) ? ----> eq(2)
If eq(1) were true then value = e^(qt) * { S/ e^(qt) - FP/ e^(rt) }
Ie value = e^(qt) * eq(2)
In other words, Spot price should be reflective of expected dividend, why are we discounting the spot price by the dividend yield for the remaining time of contract

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edupristine
Finance Junkie
Posts: 709
Joined: Wed Apr 09, 2014 6:28 am

### Re: Derivatives- Value of equity index forward formula

Hi NivethaSridhar

we are discounting the spot price by the dividend yield for the remaining time of contract because at the end of transaction we found the future price which is the amount we can get from reducing the dividend from spot price at the end of the transaction. so you have to discounting the dividend to find out the future value.