# Forward Contract

A forward contract gives linear exposure to an underlying. At expiry the payoff for the *Long* side is:

where:

N is the notional, or βleverageβ

S is the underlying price, at expiry

K is the strike price

For the *Short* side the payoff will be the exact opposite: $N(K-S)$.

As you may notice, the payoff is very similar to holding the actual underlying, for example you could buy $N$ units of the underlying paying $K$for each, and then your payoff will be similar to the *Long* side above. The main difference is that in the Forward you donβt have to actually hold the underlying as the contract can be settled directly in USD.

The forward is also very similar to the *futures contract*, which many CEXs such as FTX or Binance list for different expiries. The main difference is that the futures are standardized with margin requirements, while the forward are customizable and donβt have margining.

Note that the payoff above is that of an idealized forward, i.e. one with infinite collateral. In practice, Long and Short sides deposit an amount of collateral at the beginning, which means that the maximum profit and loss for each side are capped.

In particular, given $C_L$and $C_S$the collateral amounts deposited by the Long and Short side, the final payoff for the Long side will be:

so that the Long side can lose at most its capital, $C_L$, but the max profit is also capped at $C_S$. For the Short side itβs opposite, which can be written as $\max(-C_S, \min(C_L, N(K-S))$.

#### Example

Alice and Bob enter in a Forward contract on SOL/USD. The contract has a notional of 10 SOL (i.e. 10x leverage), and the strike is set to the current spot price, $35. Both Alice and Bob deposit 100 USDC in the contract as collateral. The duration is set to 1 week.

After 1 week has passed, the profit & loss will depend on the final price of SOL/USD:

if SOL/USD is at $40, the profit for Alice will be 10*(40-35) = $50. So she will claim 150 USDC from the contract (the original 100 USDC plus the profit). Bob will only be able to claim 50 USDC (the original 100 USDC minus the 50 loss)

if SOL/USD is at $50, the profit of Alice should be 10*(50-35) = $150, however the collateral Bob deposited was only 100 USDC, so Alice will be able to claim 200 USDC (the original 100 USDC plus the capped profit). Bob will not be able to claim anything as he lost the full collateral in the trade

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