Swap

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In finance, a swap is a derivative in which two counterparties agree to exchange one stream of cash flows against another stream. These streams are called the legs of the swap. The swap agreement defines the dates when the cash flows are to be paid and the way they are calculated.^[1] Usually at the time when the contract is initiated at least one of these series of cash flows is determined by a random or uncertain variable such as an interest rate, foreign exchange rate, equity price or commodity price.^[1]

The cash flows are calculated over a notional principal amount, which is usually not exchanged between counterparties. Consequently, swaps can be used to create unfunded exposures to an underlying asset, since counterparties can earn the profit or loss from movements in price without having to post the notional amount in cash or collateral.

Swaps can be used to hedge certain risks such as interest rate risk, or to speculate on changes in the expected direction of underlying prices.

The first swaps were negotiated in the early 1980s.^[1] David Swensen, a Yale Ph.D. at Salomon Brothers, engineered the first swap transaction according to "When Genius Failed: The Rise and Fall of Long-Term Capital Management" by Roger Lowenstein. Today, swaps are among the most heavily traded financial contracts in the world.

Swap market

Most swaps are traded over-the-counter (OTC), "tailor-made" for the counterparties. Some types of swaps are also exchanged on futures markets such as the Chicago Mercantile Exchange Holdings Inc., the largest U.S. futures market, the Chicago Board Options Exchange, IntercontinentalExchange and Frankfurt-based Eurex AG.

The Bank for International Settlements (BIS) publishes statistics on the notional amounts outstanding in the OTC derivatives market. At the end of 2006, this was USD 415.2 trillion, more than 8.5 times the 2006 gross world product. However, since the cash flow generated by a swap is equal to an interest rate times that notional amount, the cash flow generated from swaps is a substantial fraction of but much less than the gross world product -- which is also a cash-flow measure. The majority of this (USD 292.0 trillion) was due to interest rate swaps. These split by currency as:

The CDS and currency swap markets are dwarfed by the interest rate swap market. All three markets peaked in mid 2008.
Source: BIS Semiannual OTC derivatives statistics at end-December 2008

Source: "The Global OTC Derivatives Market at end-December 2004", BIS, [1], "OTC Derivatives Market Activity in the Second Half of 2006", BIS, [2]

Usually, at least one of the legs has a rate that is variable. It can depend on a reference rate, the total return of a swap, an economic statistic, etc. The most important criterion is that it comes from an independent third party, to avoid any conflict of interest. For instance, LIBOR is published by the British Bankers Association, an independent trade body.

Types of swaps

The five generic types of swaps, in order of their quantitative importance, are: interest rate swaps, currency swaps, credit swaps, commodity swaps and equity swaps. There are also many other types.

Interest rate swaps

A is currently paying floating, but wants to pay fixed. B is currently paying fixed but wants to pay floating. By entering into a interest rate swap, the net result is that each party can 'swap' their existing obligation for their desired obligation. Normally the parties do not swap payments directly, but rather, each sets up a separate swap with a financial intermediary such as a bank. In return for matching the two parties together, the bank takes a spread from the swap payments.

The most common type of swap is a “plain Vanilla” interest rate swap. It is the exchange of a fixed rate loan to a floating rate loan. The life of the swap can range from 2 years to over 15 years. The reason for this exchange is to take benefit from comparative advantage. Some companies may have comparative advantage in fixed rate markets while other companies have a comparative advantage in floating rate markets. When companies want to borrow they look for cheap borrowing i.e. from the market where they have comparative advantage. However this may lead to a company borrowing fixed when it wants floating or borrowing floating when it wants fixed. This is where a swap comes in. A swap has the effect of transforming a fixed rate loan into a floating rate loan or vice versa.

For example, party B makes periodic interest payments to party A based on a variable interest rate of LIBOR +70 basis points. Party A in turn makes periodic interest payments based on a fixed rate of 8.65%. The payments are calculated over the notional amount. The first rate is called variable, because it is reset at the beginning of each interest calculation period to the then current reference rate, such as LIBOR. In reality, the actual rate received by A and B is slightly lower due to a bank taking a spread.

Currency swaps

A currency swap involves exchanging principal and fixed rate interest payments on a loan in one currency for principal and fixed rate interest payments on an equal loan in another currency. Just like interest rate swaps, the currency swaps also are motivated by comparative advantage.

Commodity swaps

A commodity swap is an agreement whereby a floating (or market or spot) price is exchanged for a fixed price over a specified period. The vast majority of commodity swaps involve oil.

Equity Swap

An equity swap is a special type of total return swap, where the underlying asset is a stock, a basket of stocks, or a stock index. Compared to actually owning the stock, in this case you do not have to pay anything up front, but you do not have any voting or other rights that stock holders do have.

Credit default swaps

A credit default swap (CDS) is a swap contract in which the buyer of the CDS makes a series of payments to the seller and, in exchange, receives a payoff if a credit instrument - typically a bond or loan - goes into default (fails to pay). Less commonly, the credit event that triggers the payoff can be a company undergoing restructuring, bankruptcy or even just having its credit rating downgraded. CDS contracts have been compared with insurance, because the buyer pays a premium and, in return, receives a sum of money if one of the events specified in the contract occur

Other variations

There are myriad different variations on the vanilla swap structure, which are limited only by the imagination of financial engineers and the desire of corporate treasurers and fund managers for exotic structures.^[1]

• A total return swap is a swap in which party A pays the total return of an asset, and party B makes periodic interest payments. The total return is the capital gain or loss, plus any interest or dividend payments. Note that if the total return is negative, then party A receives this amount from party B. The parties have exposure to the return of the underlying stock or index, without having to hold the underlying assets. The profit or loss of party B is the same for him as actually owning the underlying asset.
• An option on a swap is called a swaption. These provide one party with the right but not the obligation at a future time to enter into a swap.
• A variance swap is an over-the-counter instrument that allows one to speculate on or hedge risks associated with the magnitude of movement, i.e. volatility, of some underlying product, like an exchange rate, interest rate, or stock index.
• A constant maturity swap, also known as a CMS, is a swap that allows the purchaser to fix the duration of received flows on a swap.
• An Amortising swap is usually an interest rate swap in which the notional principal for the interest payments declines during the life of the swap, perhaps at a rate tied to the prepayment of a mortgage or to an interest rate benchmark such LIBOR.

Valuation

The value of a swap is the net present value (NPV) of all estimated future cash flows. A swap is worth zero when it is first initiated, however after this time its value may become positive or negative.^[1] There are two ways to value swaps: in terms of bond prices, or as a portfolio of forward contracts.^[1]

Using bond prices

While principle payments are not exchanged in an interest rate swap, assuming that these are received and paid at the end of the swap does not change its value. Thus, from the point of view of the floating-rate payer, a swap can be regarded as a long position in a fixed-rate bond (i.e. receiving fixed interest payments), and a short position in a floating rate note (i.e. making floating interest payments):

V_swap = B_fixed − B_floating

From the point of view of the fixed-rate payer, the swap can be viewed as having the opposite positions. That is,

V_swap = B_floating − B_fixed

Similarly, currency swaps can be regarded as having positions in bonds whose cash flows correspond to those in the swap. Thus, the home currency value is:

V_swap = B_domestic − S₀B_foreign, where B_domestic is the domestic cash flows of the swap, B_foreign is the foreign cash flows of the swap, and S₀ is the spot exchange rate.

Using forward rate agreements

Consider a three year interest rate swap with semiannual payments. The first cash flow is known at the time the swap is initiated, however the other five exchanges can be regarded as forward rate agreements. The payment for these other exchanges is the 6 month rate observed in the market 6 months earlier. Assuming that forward interest rates are realised, this method values the swap by firstly calculating the required forward rates using the LIBOR/swap curve, then calculating the swap cash flows using these rates, and then finally discounting these cash flows back to today.

London Interbank Offered Rate (LIBOR)

LIBOR is the rate of interest offered by banks on deposit from other banks in the eurocurrency market. One-month LIBOR is the rate offered for 1-month deposits, 3-month LIBOR for three months deposits, etc. LIBOR rates are determined by trading between banks and change continuously as economic conditions change. Just like the prime rate of interest quoted in the domestic market, LIBOR is a reference rate of interest in the International Market.

Arbitrage arguments

For example, consider a plain vanilla fixed-to-floating interest rate swap where Party A pays a fixed rate, and Party B pays a floating rate. In such an agreement the fixed rate would be such that the present value of future fixed rate payments by Party A are equal to the present value of the expected future floating rate payments (i.e. the NPV is zero). Where this is not the case, an Arbitrageur, C, could:

1. assume the position with the lower present value of payments, and borrow funds equal to this present value
2. meet the cash flow obligations on the position by using the borrowed funds, and receive the corresponding payments - which have a higher present value
3. use the received payments to repay the debt on the borrowed funds
4. pocket the difference - where the difference between the present value of the loan and the present value of the inflows is the arbitrage profit.

References

• Financial Institutions Management, Saunders A. & Cornett M., McGraw-Hill Irwin 2006

See also

• Credit default swap
• Cross currency swap
• Equity swap
• Foreign exchange swap
• Constant maturity swap
• Yield curve
• Variance swap
• Interest rate swap
• Total return swap

External links

• swaps index, quantnotes.com
• swaps-rates.com, Interest swap rates statistics online
• Bank for International Settlements