Rejection sampling

Template:Expert-subject Template:Financial markets In finance, a swap is a derivative in which counterparties exchange cash flows of one party's financial instrument for those of the other party's financial instrument. The benefits in question depend on the type of financial instruments involved. For example, in the case of a swap involving two bonds, the benefits in question can be the periodic interest (coupon) payments associated with such bonds. Specifically, 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 accrued and calculated. 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 floating interest rate, foreign exchange rate, equity price, or commodity price.

The cash flows are calculated over a notional principal amount. Contrary to a future, a forward or an option, the notional amount is usually not exchanged between counterparties. Consequently, swaps can be 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.

Swaps were first introduced to the public in 1981 when IBM and the World Bank entered into a swap agreement. Today, swaps are among the most heavily traded financial contracts in the world: the total amount of interest rates and currency swaps outstanding is more thаn $348 trillion in 2010, according to Bank for International Settlements (BIS).

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, 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

	Notional outstanding in USD trillion
Currency	End 2000	End 2001	End 2002	End 2003	End 2004	End 2005	End 2006
Euro	16.6	20.9	31.5	44.7	59.3	81.4	112.1
US dollar	13.0	18.9	23.7	33.4	44.8	74.4	97.6
Japanese yen	11.1	10.1	12.8	17.4	21.5	25.6	38.0
Pound sterling	4.0	5.0	6.2	7.9	11.6	15.1	22.3
Swiss franc	1.1	1.2	1.5	2.0	2.7	3.3	3.5
Total	48.8	58.9	79.2	111.2	147.4	212.0	292.0

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 but this rate is known to be rigged (Barclays and others banks have been convicted in the 2010-2012 LIBOR scandal).

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 of swaps.

Interest rate swaps

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A is currently paying floating, but wants to pay fixed. B is currently paying fixed but wants to pay floating. By entering into an 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 return 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

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. 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 are also motivated by comparative advantage. Currency swaps entail swapping both principal and interest between the parties, with the cashflows in one direction being in a different currency than those in the opposite direction. It is also a very crucial uniform pattern in individuals and customers.

Commodity swaps

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. 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 crude oil.

Credit default swaps

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. A credit default swap (CDS) is a contract in which the buyer of the CDS makes a series of payments to the seller and, in exchange, receives a payoff if an 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. Unlike an actual insurance contract the buyer is allowed to profit from the contract and may also cover an asset to which the buyer has no direct exposure.

Subordinated risk swaps

A subordinated risk swap (SRS), or equity risk swap, is a contract in which the buyer (or equity holder) pays a premium to the seller (or silent holder) for the option to transfer certain risks. These can include any form of equity, management or legal risk of the underlying (for example a company). Through execution the equity holder can (for example) transfer shares, management responsibilities or else. Thus, general and special entrepreneurial risks can be managed, assigned or prematurely hedged. Those instruments are traded over-the-counter (OTC) and there are only a few specialized investors worldwide.

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.

• 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, 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 as the LIBOR. It is suitable to those customers of banks who want to manage the interest rate risk involved in predicted funding requirement, or investment programs.
• A Zero coupon swap is of use to those entities which have their liabilities denominated in floating rates but at the same time would like to conserve cash for operational purposes.
• A Deferred rate swap is particularly attractive to those users of funds that need funds immediately but do not consider the current rates of interest very attractive and feel that the rates may fall in future.
• An Accrediting swap is used by banks which have agreed to lend increasing sums over time to its customers so that they may fund projects.
• A Forward swap is an agreement created through the synthesis of two swaps differing in duration for the purpose of fulfilling the specific time-frame needs of an investor. Also referred to as a forward start swap, delayed start swap, and a deferred start swap.

Valuation

47 year-old Podiatrist Hyslop from Alert Bay, has lots of hobbies and interests that include fencing, property developers in condo new launch singapore and handball. Just had a family trip to Monasteries of Haghpat and Sanahin. 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. There are two ways to value swaps: in terms of bond prices, or as a portfolio of forward contracts.

Using bond prices

While principal 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 is equivalent to 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):

$V_{\mathrm {swap} }=B_{\mathrm {fixed} }-B_{\mathrm {floating} }\,$

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

$V_{\mathrm {swap} }=B_{\mathrm {floating} }-B_{\mathrm {fixed} }\,$

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:

$V_{\mathrm {swap} }=B_{\mathrm {domestic} }-S_{0}B_{\mathrm {foreign} }$, where $B_{\mathrm {domestic} }$ is the domestic cash flows of the swap, $B_{\mathrm {foreign} }$ is the foreign cash flows of the 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

As mentioned, to be arbitrage free, the terms of a swap contract are such that, initially, the NPV of these future cash flows is equal to zero. Where this is not the case, arbitrage would be possible.

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.

Subsequently, once traded, the price of the Swap must equate to the price of the various corresponding instruments as mentioned above. Where this is not true, an arbitrageur could similarly short sell the overpriced instrument, and use the proceeds to purchase the correctly priced instrument, pocket the difference, and then use payments generated to service the instrument which he is short.

See also

• Constant maturity swap
• Credit default swap
• Cross currency swap
• Equity swap
• Foreign exchange swap
• Fuel price risk management
• Interest rate swap
• PnL Explained
• Swap Execution Facility
• Total return swap
• Variance swap
• Yield curve

References

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

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External links

• swaps-rates.com, interest swap rates statistics online
• Bank for International Settlements
• International Swaps and Derivatives Association