# Value of forward contracts

At the time on entering into a forward contract, long or short, the value of the forward is zero

This is because the delivery price (K) of the asset and the forward price today (F0) remains the same

The value of the forward is basically the present value of the difference in the delivery price and the forward price

Value of a long forward, f, is given by the PV of the pay off at time T:

Æ’ = (F_{0} â€“ K )eâ€“^{rT }

K is fixed in the contract, while F_{0} keeps changing on an everyday basis

- For continuous dividend yielding underlying
- f = S
_{0}e^{-qt}â€“ Ke^{-rt}

- f = S
- For discrete dividend paying stock
- f = S
_{0}â€“ I â€“ Ke^{-rt}

- f = S
**Index futures:**A stock index can be considered as an asset that pays dividends and the dividends paid are the dividends from the underlying stocks in the index- If q is the dividend yield rate then the futures price is given as:
- F
_{0}= S0e^{(r-q)t}

**Index Arbitrage**- When F
_{0}> S_{0}e^{(r-q)T}an arbitrageur buys the stocks underlying the index and sells futures - When F
_{0}< S_{0}e^{(r-q)T}an arbitrageur buys futures and shorts or sells the stocks underlying the index

- When F