Swaps: Interest Rates, Currencies, and Credit Protection

A swapIn finance, a swap is a derivative in which two parties agree to exchange one stream of cash flows for another, based on some agreed formula. An example is a floating-for-fixed interest rate swap, which calls for (a) payments by one party based on the product of a floating interest rate and a fixed amount, called the notional, in exchange for (b) payments by the counterparty based on the product of a fixed interest rate and the same notional amount. This example illustrates the origins of the name "swap" because the instrument allows the parties to swap payment obligations based on two interest rates—a floating rate and a fixed rate.Read on Wikipedia → is a contract that exchanges one set of cash flows for another. The three kinds of swap below share one model:

trade → legs + schedule
      ├→ scheduled fixing/payment
      ├→ credit event, where applicable
      └→ market-data update → revaluation

Fixed legs and fixed-for-fixed currency swaps do not need a new rate fixing for every payment. A floating leg needs a rate fixing, a CDS needs a decision on whether a credit event happened, and any swap can be revalued when curves or exchange rates move without a cash payment occurring. The OTC market article explains how swaps can be agreed bilaterally or cleared through a central counterparty.

Store a schedule, not just a notional

A swap record normally needs:

• notional amount and currency;
• one or more payment legs;
• fixed rate or floating-rate index;
• accrual start and end dates;
• payment dates and day-count rule;
• collateral and counterparty terms;
• settlement status.

The notional is used to calculate payments. It is not automatically the current value of the swap and is not its maximum loss.

Interest-rate swap: two legs, one net payment

Suppose a company has a $100 million floating-rate loan. It enters a swap to pay fixed interest at three percent and receive the floating rate. The floating receipt offsets the floating part of the loan, so the company is left with a mostly fixed interest cost plus the loan’s spread.

For one 91-day period using an actual/360 convention, the fixed leg is:

$$\mathrm{cash\ flow} = \mathrm{notional} \times \mathrm{rate} \times \mathrm{accrual\ fraction} = \$100{,}000{,}000 \times 3\% \times \frac{91}{360} = \$758{,}333$$

If the floating rate for that period is 2.20%, the floating leg is $556,111. The fixed-rate payer therefore pays the net difference of $202,222, before other adjustments.

An overnight indexed swap (OIS) An overnight indexed swap (OIS) is an interest rate swap (IRS) over some given term, e.g. 10Y, where the periodic fixed payments are tied to a given fixed rate while the periodic floating payments are tied to a floating rate calculated from a daily compounded overnight rate over the floating coupon period. The OIS term is not overnight; it is the underlying reference rate that is an overnight rate. The exact compounding formula depends on the type of such overnight rate.Read on Wikipedia → is a version where the floating leg is calculated from overnight fixings, often compounded over the period. A missing fixing, wrong calendar, or wrong day-count rule changes the cash entry even when the notional and headline rate are correct.

A new swap is usually arranged so that the present value of the two legs is close to zero. Later, a pricing service estimates future floating fixings, discounts the scheduled cash flows, and compares the legs. The forward-pricing article explains the related idea that future cash flows need market inputs and a discounting rule.

Currency swap: the schedule has two currencies

A currency swap adds a second currency and usually exchanges principal at the start and end.

Suppose a company has borrowed €10 million but wants dollar cash flows. A simplified fixed-for-fixed currency swap can do this:

• at the start, the company pays €10 million and receives $11 million;
• during the term, it receives the euro interest and pays dollar interest;
• at the end, it returns $11 million and receives €10 million.

The euro receipt can offset the original euro loan. The dollar payment becomes the company’s effective dollar funding cost. The principal amounts are contractual amounts; the exchange rate can move during the term.

The system now needs two sets of dates, two currencies, two curves, and exchange-rate data. It must also know whether the two legs exchange principal, because that changes both cash flows and exposure. A currency swap can use fixed or floating rates on either leg.

CDS: a credit event changes the schedule

A credit default swap (CDS)A credit default swap (CDS) is a financial swap agreement that the seller of the CDS will compensate the buyer in the event of a debt default or other credit event. That is, the seller of the CDS insures the buyer against some reference asset defaulting. The buyer of the CDS makes a series of payments to the seller and, in exchange, may expect to receive a payoff if the asset defaults.Read on Wikipedia → uses a different trigger. The reference entity, the company or government whose debt the contract covers, is monitored for a defined credit event such as failure to pay, bankruptcy, or, in some contracts, restructuring. The buyer of protection pays a premium, the price of the protection, until maturity or until that event. The seller pays protection after it.

Suppose the notional is $100 million and the annual spread is 90 basis points, or 0.90 percent of the notional per year. Ignoring day-count details, a quarterly premium is:

$$\$100{,}000{,}000 \times 0.90\% \times \frac{1}{4} = \$225{,}000$$

If a cash-settlement auction sets the final debt price at 35% of face value, the simplified protection amount is:

$$\$100{,}000{,}000 \times (1 - 0.35) = \$65{,}000{,}000$$

A recovery assumption can be used to estimate the payment before the event. It should not replace the final auction or settlement price when the event has occurred. The buyer usually owes the premium accrued since the last payment date, then no later scheduled premiums are due.

A CDS can settle in cash or physically. In a physical settlement, the protection buyer delivers an eligible debt obligation under the contract rules and receives the contractual face amount from the protection seller. In a cash settlement, the seller pays the loss amount defined by the final settlement price, often determined through an auction. The settlement method is part of the contract state; it is not safe to assume that every CDS ends with the same type of payment.

For a basic system model, the important records are the reference entity, notional, spread, payment schedule, recovery assumption, credit-event status, settlement method, final settlement price, and counterparty. Advanced credit models can infer default likelihood from market prices, but that is a later modelling layer, not a prerequisite for understanding the contract.

Triggers, revaluation inputs, and risk

Instrument	Cash-flow trigger	Separate revaluation input
Interest-rate swap	Scheduled payment date; floating fixing supplies one leg	Curves and collateral terms
Currency swap	Scheduled interest and principal exchange dates	FX rate and curves
CDS	Scheduled premium dates; credit event triggers final settlement	Recovery, default assumptions, and seller credit

The common engineering problem is a scheduled cash-flow engine. The product-specific part is the event that supplies the rate, exchange rate, or credit status. The result then flows into valuation, collateral, P&L, and counterparty exposure.

Market risk and counterparty risk are different. A rate or currency move can change the replacement value of a swap; an offsetting trade can reduce that market exposure, but the counterparty may still fail while the swap has positive value to the firm. Collateral and central clearing can reduce unsecured exposure and define default procedures, but they do not make market risk or counterparty risk disappear.

Next: How Exchange-Traded Options Markets Work.