Swap Markets and Contracts

A swap is an agreement to exchange a series of future cash flows. It is the most heavily traded derivative in the world — and, once you see the trick, the easiest to value: a swap is just a portfolio of simpler instruments (bonds, currencies, stocks). This lesson prices and values interest-rate, currency, and equity swaps by replicating them with fixed- and floating-rate bonds, then covers swaptions and swap credit risk.

On this page

1 · What a swap is 3 · Types of swaps 4.1 · Swap equivalences 4.2 · Pricing interest-rate swaps 4.2.2 · Currency swaps 4.2.3 · Equity swaps 5 · Variations 6 · Swaptions 7 · Credit risk

In a swap, two parties exchange cash-flow streams on a series of future dates. The payments can be tied to an interest rate (LIBOR/Euribor), an exchange rate, an equity return, or a commodity price. By convention the party receiving floating is "long" and the party receiving fixed is "short" — though that label breaks down when both sides float. Swaps are OTC, customised, and carry default risk throughout their life.

1 · What a swap is

A swap has zero value at initiation — neither party pays the other (the one technical exception: currency swaps exchange equivalent notional principals in two currencies). Key terms:

• Settlement date — a date payments are made; the swap's value resets toward zero. Settlement period — the interval between them. Termination date — the final payment.
• Netting — if both legs are in the same currency, only the net amount changes hands, sharply reducing credit risk.
• Default risk is present whenever a payment is due, but is zero immediately after each settlement.

A swap can be terminated early by (1) paying its market value to the counterparty, (2) entering an offsetting swap, (3) selling it to a third party (rare), or (4) exercising a swaption.

3 · Types of swaps

Currency swaps

Each party makes interest payments in a different currency. Example: Target (US) wants euro funding but has a cost advantage issuing in dollars; it issues a $10m bond, then swaps with Deutsche Bank to receive dollars and pay euros — converting a dollar liability into a euro one. There are four fixed/floating combinations on each side (and reversed), and there is no natural "long/short".

Interest-rate swaps

An interest-rate swap is a currency swap where both currencies are the same — so no notional is exchanged and payments are netted. The plain-vanilla swap (one side fixed, one side floating) is the single most common derivative in the world. One side is always fixed and the other floating, or both float — but never both fixed. Example: GE borrows floating at LIBOR+25bp, then swaps to pay 6.2% fixed and receive LIBOR, locking in an all-in 6.45% fixed cost. The dealer (JPM) hedges its LIBOR exposure by selling Eurodollar futures.

Equity swaps

One leg pays the total return on a stock or index (dividends and capital gains — unlike rate or currency swaps). The return is unknown until the period ends, and can be negative — in which case the equity-return payer receives instead of pays, so a dealer paying fixed can end up making both the fixed and the equity payment. Used, e.g., to convert an equity position into fixed income without selling the stock.

Commodity and other swaps

Airlines swap to fix jet-fuel costs; miners hedge gold deliveries; parties also swap on non-storables like electricity and even weather (rainfall, snowfall).

4.1 · Swaps as combinations of simpler instruments

A swap is equivalent to a package of (a) assets — bonds, stocks, currencies; (b) forward contracts; (c) futures; or (d) options. To price and value a swap we choose the simplest replication — the underlying assets (bonds).

4.2 · Pricing and valuing interest-rate swaps

Pricing a swap means finding the fixed rate that makes its initial value zero; valuation means marking it to market later as rates move. A swap is neither asset nor liability at a zero value; positive value to one party is a liability to the other.

The floating leg is worth par

The key insight: a floating-rate note resets to its par value of 1.0 at every coupon date — each payment "grosses up" to exactly cancel the discount. So with a hypothetical $1 notional added at the end, the floating leg is worth 1.0 today. The discount factors are

Equating the fixed leg (coupons + $1 notional) to the floating leg's value of 1.0 gives the swap fixed rate:

4.2.2 · Currency swaps

Set the domestic notional at 1.0 unit; the foreign notional is \(1/S_0\) units. The fixed rate on each leg is simply that country's own plain-vanilla swap rate (using Equation 1 with that country's discount factors) — because \(1/S_0\) foreign units, converted at \(S_0\), gives exactly 1.0 domestic unit, so the present values match. Floating legs need no pricing.

4.2.3 · Equity swaps

For a pay-fixed, receive-equity swap, the fixed rate is the same Equation (1). The market value at day \(t\) is the equity-return index ratio minus the value of a fixed-rate bond:

5 · Variations of swaps

• Basis swap — both legs float (e.g. LIBOR vs T-bill); the LIBOR–T-bill gap reflects the general level of credit risk.
• Constant-maturity swap (CMS/CMT) — a leg pays a longer-maturity rate whose maturity exceeds the settlement period.
• Overnight index swap (OIS) — the floating leg compounds an overnight rate over the period.
• Amortizing / accreting swaps — the notional shrinks/grows on a schedule (index-amortizing swaps tie it to rates).
• Diff, arrears, capped, floored — cross-country single-currency floats; floating set at period end; or floating bounded above/below.

6 · Swaptions

A swaption is an option to enter a swap at a pre-agreed fixed rate. A payer swaption gives the right to pay fixed / receive floating; a receiver swaption the right to receive fixed / pay floating. They can be European or American. Used to lock a fixed rate in advance while keeping flexibility, to terminate an existing swap, or to speculate on rates.

On exercise, a swaption creates a stream of payments equal to the difference between the exercise rate \(x\) and the market swap rate, valued across the swap's payment dates:

Forward swaps are a related instrument: a binding commitment (not an option) to enter a swap later at a rate fixed today, priced off the forward — not spot — term structure, with no up-front premium.

7 · Credit risk

Only the party holding the positive-value swap bears credit risk; the underwater party owes more than it is owed. Current (immediate) credit risk is a payment due now and unpayable; potential (deferred) credit risk is the chance of future non-payment.

• For interest-rate and equity swaps (no final principal), credit risk peaks in the middle of the life. For currency swaps (notionals re-exchanged at the end), it concentrates between the middle and the end.
• The swap spread — swap fixed rate minus the default-free yield of the same maturity — reflects the general level of credit risk in the economy, not the risk of a specific swap.
• Netting (pay only the net) and marking to market (periodically settle the swap's market value and reset the fixed rate) both reduce credit risk.