Futures Path

A **futures contract** is a standardised agreement to buy or sell a specified quantity of an asset at a fixed price on a defined future date. Contracts trade on organised exchanges such as ASX 24 or CME, are guaranteed by a central counterparty, and are **marked to market** daily so gains and losses settle in cash rather than accumulating to expiry. Standardisation covers contract size, quality, delivery date, and tick size, which is what makes futures fungible and liquid in a way bilateral forwards are not.

Going **long** a futures contract means committing to buy the underlying at the agreed futures price $F_0$ on the delivery date. Going **short** means committing to sell at $F_0$. The long profits when the eventual settlement price $S_T$ rises above $F_0$, while the short profits when $S_T$ falls below $F_0$. Both sides face symmetric, theoretically unbounded payoffs because a futures contract has no premium and no embedded optionality.

The **futures payoff** is the cumulative profit or loss realised between entering the contract at price $F_0$ and the settlement price $S_T$. For a long position the payoff is $\Pi_{\text{long}} = S_T - F_0$, and for a short it is $\Pi_{\text{short}} = F_0 - S_T$. The payoff diagram is a straight line with unit slope crossing zero at $S_T = F_0$, with no premium and no embedded option, which makes futures the simplest linear derivative.

The **cost of carry** $c$ is the net cost of holding the underlying asset from today until the futures delivery date. It bundles financing cost (the risk-free rate $r$), storage and insurance for physical commodities, and subtracts any benefit from holding the asset such as dividends or **convenience yield** $q$. Under no-arbitrage the fair futures price is $F_0 = S_0 e^{(r - q)T}$ with continuous compounding, which is the engine behind both pricing and cash-and-carry arbitrage in Hull (2022) §5.4.

Under **continuous compounding** with risk-free rate $r$ and continuous income yield $q$, the no-arbitrage forward or futures price is $F_0 = S_0 e^{(r - q) T}$. The exponential factor $e^{(r-q)T}$ is the limit of $(1 + (r-q)/m)^{mT}$ as the compounding frequency $m \to \infty$, and it is the convention used throughout Hull (2022) because it linearises log returns and simplifies the Black-Scholes framework that builds on the same financing logic.

Under **discrete compounding**, the no-arbitrage futures price for an asset with no income is $F_0 = S_0 (1 + r)^T$, where $r$ is the annual rate compounded once a year. For compounding $m$ times per year the formula is $F_0 = S_0 (1 + r/m)^{mT}$. Discrete compounding is the convention used by Australian money market quotes such as **BBSW** and the **90-day bank accepted bill futures** on ASX 24, and matches how bank deposits actually accrue interest.

Futures **arbitrage** exploits any deviation between the traded futures price and the **cost-of-carry** fair value $F_0 = S_0 e^{(r - q) T}$. When the futures price is too high, a **cash-and-carry** trade buys spot, finances it at $r$, and sells futures to lock in a riskless profit. When the futures price is too low, the **reverse cash-and-carry** trade short-sells spot, invests proceeds at $r$, and buys futures. Both strategies require no net capital at inception, so any positive expected profit attracts traders until the gap closes.

As a futures contract approaches its last trading day, the futures price $F_t$ converges to the spot price $S_t$, so at expiry $F_T = S_T$. The mechanism is **arbitrage**. Any positive gap would let a trader sell futures and buy spot, deliver immediately, and pocket the difference. The same logic in reverse closes any negative gap. **Basis**, defined as $b_t = S_t - F_t$, collapses to zero at the last settlement, which is the foundation of hedge accuracy.

The **effective price** is the net price a hedger actually realises after combining the physical market transaction with the offsetting futures hedge gain or loss. For a short hedge, it equals the initial futures price $F_1$ plus the **basis** at close-out, $P_{\text{eff}} = F_1 + (S_2 - F_2)$. For a long hedge, $P_{\text{eff}} = F_1 - (F_2 - S_2)$. The effective price equals $F_1$ only when basis is zero at close-out, which happens automatically at expiry for a matched contract but rarely at any earlier date.

**Initial margin** is the cash or eligible collateral a trader must deposit with the broker and the **clearing house** to open a futures position. It is a **performance bond**, not a purchase price, calibrated to cover a worst-case daily price move with high statistical confidence. ASX Clear (Futures) sets initial margins using a SPAN-style model targeting the larger of three standard deviations of the 60-day and 252-day historical price distribution, which under normal market conditions covers roughly 99.7 per cent of expected daily moves.

**Maintenance margin** is the minimum equity balance that must remain in a futures margin account. If accumulated losses drag the balance below this floor, the clearing broker issues a **margin call** requiring the trader to top the account back up to the **initial margin** level, not just to the maintenance threshold. Maintenance margin is typically set at $70\%$ to $80\%$ of initial margin and creates a buffer absorbing routine daily moves before any cash injection is triggered.

**Variation margin** is the cash transferred between counterparties each day to reflect the change in the futures settlement price. For a long position with $N$ contracts, the daily flow is $VM_t = (F_t - F_{t-1}) \times \text{multiplier} \times N$. Losses leave the margin account, gains enter it, and the running balance funds the clearing house's daily **mark-to-market** mechanism. Variation margin is the operational expression of marking to market and is distinct from initial and maintenance margin, which are static buffers.

**Marking to market** is the daily process by which the clearing house revalues every open futures position at the exchange settlement price and settles the cash difference through margin accounts. Gains are credited and losses are debited the same evening or the next morning, so unrealised profit and loss never accumulates. This **daily settlement** is the operational mechanism that lets futures support far larger leverage than forwards while keeping counterparty credit exposure to roughly one day of price movement.

A **margin call** is the broker's demand for additional collateral when accumulated losses pull a futures account below the **maintenance margin** threshold. The trader must restore the balance to the **initial margin** level, not merely to the maintenance line, usually within one business day. Failure to meet the call gives the broker the right to **close out** (liquidate) the position at the prevailing market price, with any residual loss still owed by the trader.

**Closing out** a futures position means entering an equal and offsetting trade in the same contract to bring net exposure to zero. A long position is closed by selling the same contract; a short is closed by buying it back. Closing out is the standard way to exit a futures trade because more than ninety-five per cent of contracts never reach physical or final cash delivery. After close-out, any remaining margin balance is returned to the trader and no further variation margin flows occur.

The **tick** is the minimum price change allowed for a futures contract, fixed by the exchange in the contract specifications. The **tick value** is the dollar gain or loss per contract for a one-tick move, equal to the tick size multiplied by the contract size or multiplier. Knowing the tick value converts a quoted price change into a precise cash flow, which is the building block of every futures P&L, margin, and risk calculation.