3.1.2 Introduction to Forward and Futures

2. Introduction to Forward and Futures

2.1 Basics of Derivatives

2.1.1 Definition of Derivative

Derivatives are contracts whose values depend on the values of one or more financial variables (e.g., equity prices, exchange rates, and interest rates). These variables are referred to as underlying asset.

The underlying assets include:

• Financial asset: equity, fixed-income security, currency;
• Physical asset: commodity;
• Other: interest rate, credit, weather, other derivatives, etc.

Derivatives are created in the form of legal contracts.

• The long: buyer, holder
• The short: seller, writer

2.1.2 Linear and Non-linear Derivatives

Derivatives can be categorized into linear and non-linear products. Linear derivatives provide a payoff that is linearly related to the value of the underlying asset(s).

Forward, Futures and Swap contracts are an example of linear derivatives.

Options are non-linear derivatives because their payoff is a non-linear function of the value of their underlying assets.

2.1.3 Market participants

Derivatives are versatile instruments that can be used for hedging, speculation, or arbitrage.

Hedgers: reduce risk, transfer risk

Speculators: actively take risk to make profit

Arbitrageurs: make risk-less profit (arbitrage opportunity)

2.2 Forward and Futures

2.2.1 Forward Contracts

Forward contract is an over-the-counter derivative contract, in which two parties agree that the buyer will purchase an underlying asset from the seller at a later date at a fixed price (forward price) they agree on when the contract is signed.

In addition to the (forward) price, the two parties also agree on several other matters, such as the identity and the quantity of the underlying.

2.2.2 Forward Payoff

$S_T$ is the asset price at the maturity of a forward contract.
$F_0(T)$ is the delivery price (i.e., the forward price when the contract was initiated).

The payoff from a long forward contract on one unit of the asset is $S_T-F_0(T)$.
The payoff from a short forward contract on one unit of the asset is $F_0(T)—S_T$.

2.2.3 Future Contracts

Futures contracts are specialized forward contracts that have been standardized and trade on a futures exchange.

The exchange offers a facility in the form of a physical location and/or an electronic system as well as liquidity provided by authorized market makers.

Futures contracts have specific underlying assets, times to expiration, delivery and settlement conditions, and quantities.

Futures trade on a wide range of other underlying assets. This includes:

• corn, wheat, and live cattle
• gold, silver, copper, and platinum
• S&P 500 and the Nasdaq 100
• oil, natural gas, and electricity
• real estate indices
• cryptocurrencies like bitcoin

2.2.4 Future Payoff

$F_t(T)$ is the futures price when the contract is closed at time $t$.
$F_0(T)$ is the futures price at time $0$ (the futures price when the contract was initiated).

The payoff from a long futures contract on one unit of the asset is $F_t(T)—F_0(T)$.
The payoff from a short futures contract on one unit of the asset is $F_0(T)—F_t(T)$.

Forward	Futures
Private traded	Exchange-traded
Unique customized contracts	Standardized contracts
Default risk is present	Guaranteed by clearinghouse
Little or no regulation	Regulated
No margin deposit required	Margin required and adjusted
Settlement at maturity	Daily settlement (mark to market)
Delivery usually happens	Closed out before maturity