## Swap Finance Libor Homework

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A **swap** is a derivative contract where two parties exchange financial instruments.^{[1]} Most swaps are derivatives in which two counterpartiesexchange cash flows of one party's financial instrument for those of the other party's financial instrument.^{[1]} 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.^{[2]} Usually at the time when the contract is initiated, at least one of these series of cash flows is determined by an uncertain variable such as a floating interest rate, foreign exchange rate, equity price, or commodity price.^{[2]}

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.^{[3]}

Swaps were first introduced to the public in 1981 when IBM and the World Bank entered into a swap agreement.^{[4]} 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 than $348 trillion in 2010, according to Bank for International Settlements (BIS).^{[citation needed]}

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:

Currency | Notional outstanding (in USD trillion) | ||||||
---|---|---|---|---|---|---|---|

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 Intercontinental Exchange.

## Size of the Swap Market[edit]

As the International Finance in Practice box suggests, the market for currency swaps developed first. Today, however, the interest rate swap market is larger. Size is measured by **notional principal**, a reference amount of principal for determining interest payments. The exhibit indicates that both markets have grown significantly since 2000, but that the growth in interest rate swap has been by far more dramatic. The total amount of interest rate swaps outstanding increased from $48,768 billion at year-end 2000 to $349.2 trillion by year-end 2009, an increase of 616 percent. Total outstanding currency swaps increased 417 percent, from $3,194 billion at year-end 2000 to over $16.5 trillion by year-end 2009.^{[citation needed]}

## The Swap Bank[edit]

A swap bank is a generic term to describe a financial institution that facilitates swaps between counterparties. A swap bank can be an international commercial bank, an investment bank, a merchant bank, or an independent operator. The swap bank serves as either a swap broker or swap dealer. As a broker, the swap bank matches counterparties but does not assume any risk of the swap. The swap broker receives a commission for this service. Today, most swap banks serve as dealers or market makers. As a market marker, the swap bank stands willing to accept either side of a currency swap, and then later lay it off, or match it with a counterparty. In this capacity, the swap bank assumes a position in the swap and therefore assumes certain risks. The dealer capacity is obviously more risky, and the swap bank would receive a portion of the cash flows passed through it to compensate it for bearing this risk.^{[citation needed]}

## Is the Swap Market efficient?[edit]

The two primary reasons for a counterparty to use a currency swap are to obtain debt financing in the swapped currency at an interest cost reduction brought about through comparative advantages each counterparty has in its national capital market, and/or the benefit of hedging long-run exchange rate exposure. These reasons seem straightforward and difficult to argue with, especially to the extent that name recognition is truly important in raising funds in the international bond market. The two primary reasons for swapping interest rates are to better match maturities of assets and liabilities and /or to obtain a cost savings via the quality spread differential (QSD). In an efficient market without barriers to capital flows, the cost-savings argument through a QSD is difficult to accept. It implies that an arbitrage opportunity exists because of some mispricing of the default risk premiums on different types of debt instruments. If the QSD is one of the primary reasons for the existence of interest rate swaps, one would expect arbitrage to eliminate it over time and that the growth of the swap market would decrease. Thus, the arbitrage argument does not seem to have much merit. Consequently, one must rely on an argument of market completeness for the existence and growth of interest rate swaps. That is, all typesof debt instruments are not regularly available for all borrowers. Thus, the interest rate swap market assists in tailoring financing to the type desired by a particular borrower. Both counterparties can benefit (as well as the swap dealer) through financing that is more suitable for their asset maturity structures.^{[citation needed]}

## Types of swaps[edit]

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[edit]

Main article: Interest rate swap

The most common type of swap is an interest rate swap. 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[edit]

Main article: Currency swap

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[edit]

Main article: Commodity swap

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.

### Subordinated risk swaps[edit]

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[edit]

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.^{[2]}

- 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[edit]

Further information: Rational pricing § Swaps, and Arbitrage

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.^{[2]} There are two ways to value swaps: in terms of bond prices, or as a portfolio of forward contracts.^{[2]}

Note that the discussion below is representative of pure rational pricing; however, insofar as it excludes credit risk, it is somewhat *idealized*. Current practice - i.e. since the 2007–2012 global financial crisis - is to price swaps under a "multi-curve" framework; see Interest rate swap #Valuation and pricing for formulae, and Financial economics #Derivative pricing for context.

### Using bond prices[edit]

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):

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

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:

- , where is the domestic cash flows of the swap, 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[edit]

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:

- assume the position with the
*lower*present value of payments, and borrow funds equal to this present value - meet the cash flow obligations on the position by using the borrowed funds, and receive the corresponding payments - which have a higher present value
- use the received payments to repay the debt on the borrowed funds
- 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[edit]

## References[edit]

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

## External links[edit]

*Source: BIS Semiannual OTC derivatives statistics at end-December 2008*

Problem 7.16 CB Solutions Assumptions Values Notional principal $ 5,000,000 LIBOR, per annum 4.000% Spread paid over LIBOR, per annum 2.000% Swap rate, to pay fixed, per annum 7.000% First Second Third Fourth 6-months 6-months 6-months 6-months a. LIBOR increases 50 basis pts/6 months 0.500% Expected LIBOR 4.500% 5.000% 5.500% 6.000% Current loan agreement: Expected LIBOR (for 6 months)-2.250%-2.500%-2.750%-3.000% Spread (for 6 months)-1.000%-1.000%-1.000%-1.000% Expected interest payment-3.250%-3.500%-3.750%-4.000% Swap Agreement: Pay fixed (for 6-months)-3.500%-3.500%-3.500%-3.500% Receive floating (LIBOR for 6 months) 2.250% 2.500% 2.750% 3.000% Net interest (loan + swap)-4.500%-4.500%-4.500%-4.500% Swap savings? Net interest after swap $ (225,000) $ (225,000) $ (225,000) $ (225,000) Loan agreement interest (162,500) (175,000) (187,500) (200,000) Swap savings (swap cost) $ (62,500) $ (50,000) $ (37,500) $ (25,000) b. LIBOR decreases 25 basis pts/6 months-0.250% Expected LIBOR 3.750% 3.500% 3.250% 3.000% Current loan agreement: Expected LIBOR (for 6 months)-1.875%-1.750%-1.625%-1.500% Spread (for 6 months)-1.000%-1.000%-1.000%-1.000% Expected interest payment-2.875%-2.750%-2.625%-2.500% Swap Agreement: Pay fixed (for 6-months)-3.500%-3.500%-3.500%-3.500% Receive floating (LIBOR for 6 months) 1.875% 1.750% 1.625% 1.500% Net interest (loan + swap)-4.500%-4.500%-4.500%-4.500% Swap savings? Net interest after swap $ (225,000) $ (225,000) $ (225,000) $ (225,000) Loan agreement interest (143,750) (137,500) (131,250) (125,000) Swap savings (swap cost) $ (81,250) $ (87,500) $ (93,750) $ (100,000) In both cases CB Solutions is suffering higher total interest costs as a result of the swap. Heather O'Reilly, the treasurer of CB Solutions, believes interest rates are going to rise, so she wants to swap her future floating rate interest payments for fixed rates. At present she is paying LIBOR + 2% per annum on $5,000,000 of debt for the next two years, with payments due semiannually. LIBOR is currently 4.00% per annum. Ms. O'Reilly has just made an interest payment today, so the next payment is due six months from today. Ms. O'Reilly finds that she can swap her current floating rate payments for fixed payments of 7.00% per annum. (CB Solution’s weighted average cost of capital is 12%, which Ms. O'Reilly calculates to be 6% per six month period, compounded semiannually). a. If LIBOR rises at the rate of 50 basis points per six month period, starting tomorrow, how much does Ms. O'Reilly save or cost her company by making this swap? b. If LIBOR falls at the rate of 25 basis points per six month period, starting tomorrow, how much does Ms. O'Reilly save or cost her company by making this swap?

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