DER 2 Forward Commitment and Contingent Claim Features and Instruments

A derivative draws its value from something else: an underlying asset or index, or another financial variable such as the volatility of an equity price. Two broad families cover almost every contract you will meet. In a firm commitment, both counterparties are obligated to exchange a predetermined amount at settlement. In a contingent claim, one counterparty gets to decide whether, and sometimes when, the trade settles at all.

Forwards, futures, and swaps are firm commitments: each side must perform, exchanging an underlying in the future at a price fixed today. Because the value moves one-for-one with the underlying, these contracts have a symmetric payoff and are called linear derivatives. Options are the most common contingent claim. The buyer pays a premium for a right, not an obligation, so the payoff bends at the exercise price and can never turn negative for the buyer. That kink makes the payoff asymmetric, which is why contingent claims are described as non-linear derivatives.

The two families are not rivals. A firm commitment and a contingent claim can be arranged to give a similar directional exposure to the same underlying, yet their payoff and profit shapes differ in ways that matter for risk. The rest of this lesson defines each instrument, shows how to value it at maturity, and then places the linear and non-linear profiles side by side.

A forward contract is an OTC agreement between two parties: at a future date the buyer takes delivery of an underlying from the seller at a fixed price set today. OTC terms can be tailored to the size, underlying, maturity, and credit arrangements each side wants, which is why an end user hedging a specific exposure often prefers a forward. That flexibility comes at a cost: OTC contracts usually carry more counterparty risk than an exchange-traded equivalent. An importer, for instance, might buy foreign currency forward to lock in the cost of a future goods delivery. The forward buyer holds a long position and gains when the underlying appreciates over the life of the contract.

Suppose the deal is agreed now, at time t = 0, with maturity at time T. No money changes hands at the start. The two sides simply commit to trade the underlying at maturity for a forward price written F0(T), where the subscript marks the date the price is fixed and the term in parentheses marks the delivery date. Let ST be the spot price of the underlying at maturity. Because nothing is paid upfront, the buyer’s payoff equals the buyer’s profit.

The buyer gains if the underlying can be taken at a market value ST above the agreed price F0(T). If instead F0(T) exceeds ST, the buyer loses the difference, either taking delivery at an above-market price or paying the seller that amount in cash. The seller’s outcome is the mirror image. This straight-line, equal-and-opposite result is the symmetric payoff typical of firm commitments.

A contract may call for physical delivery of the underlying or for cash settlement of the difference. Either way the buyer receives [ST − F0(T)] and the seller receives the negative of that. To build the same long exposure in the cash market, a buyer would instead pay S0 today and earn (ST − S0) by maturity.

Futures contracts are forwards with standardized sizes, dates, and underlyings that trade on a futures exchange. The exchange sets contract details based on buyer and seller interest, and the combination of uniform terms, an organized market, and a central clearing facility delivers both liquidity and protection against default. The buyer takes a long exposure by agreeing to purchase the underlying later at the futures price f0(T); the seller takes the opposite short exposure.

Daily settlement and margin

What sets futures apart is that gains and losses are settled every day, backed by the clearinghouse guarantee. At each session’s end the clearinghouse takes an average of the final trading prices, names it the settlement price, and marks every contract to it. This process is called mark to market (MTM), or the daily settlement. As with forwards, no cash moves when the contract opens, but each side must deposit an initial margin into a futures margin account at the exchange, from which the clearinghouse settles the daily marks. Each contract also sets a maintenance margin, a floor below the initial margin that the balance must not breach. The clearinghouse moves funds daily, crediting accounts with MTM gains and charging those with MTM losses.

If a loss pushes the balance below the maintenance margin, the holder receives a margin call and must immediately restore the account to the initial margin. The top-up amount is called variation margin. A counterparty that fails to meet a call must close its position as soon as possible and cover any further loss; if it cannot, the clearinghouse covers the shortfall from an insurance fund it maintains.

Trading rules, close-out, and delivery

Exchanges can impose stricter terms to limit default risk, for example raising margins or making intraday calls when a position is large or volatility jumps. Some contracts also cap daily moves with price limits, a band around the previous settlement price within which trades must occur; if participants want to trade outside the band, trading halts until two parties agree within range. A related tool, the circuit breaker, pauses trading briefly when a limit is reached. The number of contracts still open, the open interest, is settled at maturity by cash or physical delivery, though a holder can close out earlier by taking an offsetting position, such as a buyer selling the open contract. With physical delivery the seller must supply an underlying of specified type, quantity, and quality at a set location and the buyer must accept and pay, which forces the futures price to converge to the spot price at expiration.

The net payoff of a future matches that of a forward with the same maturity; only the timing of cash flows differs, because the future settles a little each day rather than all at once. By the time value of money the two streams are not strictly equal, but for short maturities and low rates the gap is small. Note also that under the forward the intermediary bears counterparty risk to Procam, whereas margining removes most of that risk on the future; in practice intermediaries often apply collateral arrangements to forwards for the same reason.

A swap is a firm commitment under which two counterparties exchange a series of cash flows over time. One leg is typically variable, or floating, set by a market reference rate that resets each period; the other is usually fixed, though it can instead track a different rate or asset. The side paying the variable leg is the floating-rate payer (equivalently the fixed-rate receiver), and the side paying the fixed leg is the fixed-rate payer (the floating-rate receiver). Interest rate swaps that exchange fixed for floating are by far the most common. Each period the market reference rate (MRR) on the floating leg resets while the fixed leg, called the swap rate, stays constant, so a swap behaves like a bundle of forward exchanges lined up across future dates.

Counterparties normally settle a single net payment each period rather than exchanging both legs in full.

This is how a manager can change portfolio duration without buying or selling bonds, and how an issuer can reshape the exposure of a liability such as a term loan. As with forwards and futures, no money changes hands at inception, so the value of a swap starts at effectively zero net of transaction costs. Because implied forward rates can be derived from spot rates, the forward MRRs supply the expected floating cash flows, and the swap rate is the single constant fixed yield that sets the present value of the fixed leg equal to the present value of the floating leg.

As rates move and time passes, the mark-to-market value of a swap drifts away from zero, positive for one side and equally negative for the other. Credit terms are privately negotiated and range from fully uncollateralized exposure to futures-style margining for one or both sides. A default usually triggers termination and MTM settlement, as with any debt claim. Swaps cleared through a central counterparty (CCP) add margin provisions similar to futures to standardize and cut counterparty risk.

A contingent claim is a contract in which one counterparty holds the right to decide whether the trade settles, based on the value of the underlying. The option is the most common example. Like a forward, an option specifies an underlying, a contract size, a pre-agreed price, and a maturity, but here the buyer holds the right and not the obligation to transact, while the seller is obliged to perform if the buyer chooses to. As a result the option buyer’s payoff is always zero or positive, never negative.

The premium and the exercise decision

Suppose a buyer pays a premium c0 of USD5 at t = 0 for the right, but not the obligation, to buy stock S at time T for a pre-agreed price X of USD30. The buyer’s choice at maturity turns on the stock price ST. If ST = USD40, the buyer exercises, buys at USD30, and gains USD10 (40 − 30) on the transaction, for a profit of USD5 after the premium. If ST = USD25, the buyer walks away rather than overpay, losing only the USD5 premium. The decision to transact is called exercise, and the pre-agreed price X is the exercise price or strike price. The right to exercise is what the upfront premium buys. This lesson uses European options, which can be exercised only at maturity; American options, by contrast, can be exercised any time up to maturity. The labels describe the timing of exercise, not any geography.

The two basic types are the call, a right to buy the underlying, and the put, a right to sell it. A buyer exercises either one only when doing so returns a positive payoff; otherwise the option expires worthless and the buyer loses the premium. Before maturity, part of an option’s value is its intrinsic value, the exercise value at that moment. A call is in-the-money when the spot St exceeds X, with intrinsic value (St − X). When St is below X the call is out-of-the-money, and when St equals X it is at-the-money; in both of those cases intrinsic value is zero and the price ct is all time value.

Long call

A call buyer profits when the underlying rises. The value at maturity and the profit are:

An option’s remaining time to maturity adds a second component beyond intrinsic value. The longer that time, the greater the chance of a favorable move that lifts both the likelihood and the size of a profitable exercise. This time value is always positive and decays to zero as maturity arrives.

Short call, and one-sided credit risk

The call seller is the buyer’s mirror image: the most the seller can make is the premium, while the loss grows without limit as the underlying climbs above X. This asymmetry also shapes credit risk. Once the premium is paid, the seller has no credit exposure to the buyer, but the buyer bears the seller’s credit risk equal to the payoff owed at maturity, so counterparty risk on an option is one-sided.

Long and short put

A put buyer benefits from a falling underlying, exercising the right to sell at X only when ST is below X. The long put value and profit are:

A put seller earns at most the premium, like a call seller, but the put seller’s loss is bounded because the underlying cannot fall below zero. The short put payoff and profit are the negatives of the buyer’s:

A credit derivative is built on a credit underlying, meaning the default risk of one debt issuer, or of a basket of issuers grouped into an index. The most common is the credit default swap (CDS), which lets an investor manage the risk of loss from an issuer’s default separately from holding the cash bond. A CDS trades on a credit spread, much like a cash bond, and that spread reflects the chance of default (POD) together with the loss given default (LGD). A wider spread signals greater distress and goes hand in hand with a lower cash bond price, while a narrower spread pairs with a higher one.

Despite the name, a CDS is a contingent claim that borrows features from firm commitments. Unlike a call or a put, both the timing of exercise and the payment on exercise depend on what happens to the underlying issuer. As with a plain interest rate swap, a CDS struck at a par spread has zero net present value, and the notional is not exchanged but simply scales the spread and settlement amounts.

Protection buyer and seller

Under the contract, the protection buyer pays the protection seller to shoulder the loss that would follow if a third-party issuer defaults. A credit event, usually defined as bankruptcy, failure to pay, or an involuntary restructuring, obliges the seller to pay the buyer to settle. That contingent payment equals the issuer’s loss given default applied to the contract notional. The reference credit can be a corporate or a sovereign name, a whole index of issuers, or a special purpose vehicle holding a pool of loans, mortgages, or bonds.

A buyer with an existing bond exposure can use a CDS as a hedge that works like insurance: a credit event that cuts the bond’s value is offset by the CDS payment. A buyer without that underlying exposure is instead positioning to gain from wider spreads and lower bond prices, and so is short credit risk. The seller collects a periodic fixed spread in return for the contingent obligation, an arrangement close to writing insurance, and so it stands much like a holder taking long risk on the issuer’s own debt. Between inception and any credit event, the mark-to-market change on a CDS can be approximated the same way as for any fixed-income instrument:

A firm commitment forces both sides to perform, while an option buyer decides at maturity whether to perform, based on the underlying relative to the exercise price. The two can be arranged to give a similar directional bet, yet their profit shapes differ. Consider a case where the strike X is set to match the forward price F0(T), so both contracts share the same reference level.

Long forward against long call

Both a long forward and a long call gain as the underlying rises. The forward profit is the straight line [ST − F0(T)]. For a call struck at F0(T), the profit is:

Comparing the two profits, [ST − F0(T)] against −c0, gives a clean ranking:

• If ST − F0(T) > −c0, the forward profit exceeds the call profit.
• If ST − F0(T) = −c0, the two profits are equal.
• If ST − F0(T) < −c0, the call profit exceeds the forward profit.

Read together, the long call looks like a long position in the underlying with built-in downside protection, bought in exchange for the premium.

Long forward against short put

A sold put is another position that gains when the underlying rises, though its upside is capped at the premium received. Against a long forward, with the same modified exercise price, the short put profit is:

Setting the forward profit equal to the short put profit gives the mirror ranking:

• If ST − F0(T) > p0, the forward profit exceeds the option profit.
• If ST − F0(T) = p0, the two profits are equal.
• If ST − F0(T) < p0, the option profit exceeds the forward profit.

Here the sold put resembles a long position in the underlying that gives up its price appreciation in return for the premium. The deeper symmetry linking long call, short put, and long forward is developed in a later lesson. For the opposite direction, a short forward, a short call, and a long put all gain when the underlying falls.