Swaption
Encyclopedia
A swaption is an option
granting its owner the right but not the obligation to enter into an underlying swap
. Although options can be traded on a variety of swaps, the term "swaption" typically refers to options on interest rate swap
s.
There are two types of swaption contracts:
The buyer and seller of the swaption agree on:
arising from their core business or from their financing arrangements. For example, a corporation wanting protection from rising interest rates might buy a payer swaption. A bank that holds a mortgage portfolio might buy a receiver swaption to protect against lower interest rates that might lead to early prepayment of the mortgages. A hedge fund believing that interest rates will not rise by more than a certain amount might sell a payer swaption, aiming to make money by collecting the premium. Major investment and commercial banks such as JP Morgan Chase, Bank of America Securities and Citigroup make markets in swaptions in the major currencies, and these banks trade amongst themselves in the swaption interbank market. The market making banks typically manage large portfolios of swaptions that they have written with various counterparties. A significant investment in technology and human capital is required to properly monitor the resulting exposure. Swaption markets exist in most of the major currencies in the world, the largest markets being in U.S. dollars, euro, sterling and Japanese yen.
The swaption market is over-the-counter
(OTC), i.e., not traded on any exchange. Legally, a swaption is an agreement between the two counterparties to exchange the required payments. The counterparties are exposed to each others' failure to make scheduled payments on the underlying swap, although this exposure is typically mitigated through the use of "collateral agreements" whereby margin is posted to cover the anticipated future exposure.
s, in some cases. The standard varieties are
The valuation of Swaptions is complicated in that the at-the-money level is the forward swap rate, being the forward rate
that would apply between the maturity of the option - time m - and the tenor of the underlying swap such that the swap, at time m, would have an "NPV
" of zero; see swap valuation. Moneyness, therefore, is determined based on whether the strike rate is higher, lower, or at the same level as the forward swap rate.
Addressing this, quantitative analyst
s value swaptions by constructing complex lattice-based
term structure
and short rate
models that describe the movement of interest rates over time.http://books.google.com/books?id=wF8yVzLI6EYC&printsec=frontcover&dq=Valuation+of+fixed+income+securities+and+derivatives http://pages.stern.nyu.edu/~eelton/debt_inst_class/option%20valuation.pdf However, a standard practice, particularly amongst traders
, to whom speed of calculation is more important, is to value European swaptions using the Black model
. For American- and Bermudan- styled options
, where exercise is permitted prior to maturity, only the lattice based approach is applicable.
in 1983. Lawton was the Head Trader for Fixed Income Derivatives at First Interstate Bank
in Los Angeles
at that time. Lawton worked with First Interstate's Treasury Options Desk to adapt the concept of an interest rate swap and an options contract. The swaption was for a period of one year. First Interstate, for a premium, sold a Los Angeles based savings and loan the right to enter into a five-year interest rate swap to pay fixed versus three-month Libor on a notional amount of $5 million [source needed]
Tools
Option (finance)
In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...
granting its owner the right but not the obligation to enter into an underlying swap
Swap (finance)
In finance, a swap is a derivative in which counterparties exchange certain benefits 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...
. Although options can be traded on a variety of swaps, the term "swaption" typically refers to options on interest rate swap
Interest rate swap
An interest rate swap is a popular and highly liquid financial derivative instrument in which two parties agree to exchange interest rate cash flows, based on a specified notional amount from a fixed rate to a floating rate or from one floating rate to another...
s.
There are two types of swaption contracts:
- A payer swaption gives the owner of the swaption the right to enter into a swap where they pay the fixed leg and receive the floating leg.
- A receiver swaption gives the owner of the swaption the right to enter into a swap in which they will receive the fixed leg, and pay the floating leg.
The buyer and seller of the swaption agree on:
- the premium (price) of the swaption
- the strike rate (equal to the fixed rate of the underlying swap)
- length of the option period (which usually ends two business days prior to the start date of the underlying swap),
- the term of the underlying swap,
- notional amount,
- amortization, if any
- frequency of settlement of payments on the underlying swap = basis point spread
The swaption market
The participants in the swaption market are predominantly large corporations, banks, financial institutions and hedge funds. End users such as corporations and banks typically use swaptions to manage interest rate riskInterest rate risk
Interest rate risk is the risk borne by an interest-bearing asset, such as a loan or a bond, due to variability of interest rates. In general, as rates rise, the price of a fixed rate bond will fall, and vice versa...
arising from their core business or from their financing arrangements. For example, a corporation wanting protection from rising interest rates might buy a payer swaption. A bank that holds a mortgage portfolio might buy a receiver swaption to protect against lower interest rates that might lead to early prepayment of the mortgages. A hedge fund believing that interest rates will not rise by more than a certain amount might sell a payer swaption, aiming to make money by collecting the premium. Major investment and commercial banks such as JP Morgan Chase, Bank of America Securities and Citigroup make markets in swaptions in the major currencies, and these banks trade amongst themselves in the swaption interbank market. The market making banks typically manage large portfolios of swaptions that they have written with various counterparties. A significant investment in technology and human capital is required to properly monitor the resulting exposure. Swaption markets exist in most of the major currencies in the world, the largest markets being in U.S. dollars, euro, sterling and Japanese yen.
The swaption market is over-the-counter
Over-the-counter (finance)
Within the derivatives markets, many products are traded through exchanges. An exchange has the benefit of facilitating liquidity and also mitigates all credit risk concerning the default of a member of the exchange. Products traded on the exchange must be well standardised to transparent trading....
(OTC), i.e., not traded on any exchange. Legally, a swaption is an agreement between the two counterparties to exchange the required payments. The counterparties are exposed to each others' failure to make scheduled payments on the underlying swap, although this exposure is typically mitigated through the use of "collateral agreements" whereby margin is posted to cover the anticipated future exposure.
Properties
From the point of view of the payer, swaptions increase in value with the volatility of the underlying swap rate, with curve steepness, and with the absolute level of the rate curve. For the receiver, the opposite is true. As with any other option, if the swaption is not exercised by maturity, it expires worthless.Swaption styles
There are three main categories of Swaption, although exotic desks may be willing to create customised types, analgous to exotic optionExotic option
In finance, an exotic option is a derivative which has features making it more complex than commonly traded products . These products are usually traded over-the-counter , or are embedded in structured notes....
s, in some cases. The standard varieties are
- Bermudan swaption, in which the owner is allowed to enter the swap on multiple specified dates.
- European swaption, in which the owner is allowed to enter the swap only on the maturity date.
- American swaption, in which the owner is allowed to enter the swap on any day that falls within a range of two dates.
Valuation
- Compare: Bond option: Valuation
The valuation of Swaptions is complicated in that the at-the-money level is the forward swap rate, being the forward rate
Forward rate
The forward rate is the future yield on a bond. It is calculated using the yield curve. For example, the yield on a three-month Treasury bill six months from now is a forward rate.-Forward rate calculation:...
that would apply between the maturity of the option - time m - and the tenor of the underlying swap such that the swap, at time m, would have an "NPV
Net present value
In finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...
" of zero; see swap valuation. Moneyness, therefore, is determined based on whether the strike rate is higher, lower, or at the same level as the forward swap rate.
Addressing this, quantitative analyst
Quantitative analyst
A quantitative analyst is a person who works in finance using numerical or quantitative techniques. Similar work is done in most other modern industries, but the work is not always called quantitative analysis...
s value swaptions by constructing complex lattice-based
Lattice model (finance)
In finance, a lattice model can be used to find the fair value of a stock option; variants also exist for interest rate derivatives.The model divides time between now and the option's expiration into N discrete periods...
term structure
Yield curve
In finance, the yield curve is the relation between the interest rate and the time to maturity, known as the "term", of the debt for a given borrower in a given currency. For example, the U.S. dollar interest rates paid on U.S...
and short rate
Short rate model
In the context of interest rate derivatives, a short-rate model is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written r_t \,.-The short rate:...
models that describe the movement of interest rates over time.http://books.google.com/books?id=wF8yVzLI6EYC&printsec=frontcover&dq=Valuation+of+fixed+income+securities+and+derivatives http://pages.stern.nyu.edu/~eelton/debt_inst_class/option%20valuation.pdf However, a standard practice, particularly amongst traders
Trader (finance)
A trader is someone in finance who buys and sells financial instruments such as stocks, bonds, commodities and derivatives. A broker who simply fills buy or sell orders is not a trader, as they are merely executing instructions given to them. According to the Wall Street Journal in 2004, a managing...
, to whom speed of calculation is more important, is to value European swaptions using the Black model
Black model
The Black model is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing bond options, interest rate caps / floors, and swaptions...
. For American- and Bermudan- styled options
Option style
In finance, the style or family of an option is a general term denoting the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American options. These options - as well as others where the...
, where exercise is permitted prior to maturity, only the lattice based approach is applicable.
- To use the lattice based approach, the analyst constructs a "tree" of short rates consistent with today's yield curveYield curveIn finance, the yield curve is the relation between the interest rate and the time to maturity, known as the "term", of the debt for a given borrower in a given currency. For example, the U.S. dollar interest rates paid on U.S...
and short rate (caplet) volatility, and where the final time step of the tree corresponds to the date of the underlying swap's maturity. Models commonly used here are Black-Derman-Toy and Hull-White. Using this tree, (1) the swap is valued at each node by "stepping backwards" through the tree, where at each node, its value is the discountedPresent valuePresent value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...
expected valueExpected valueIn probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...
of the up- and down-nodes in the later time step, added to which is the discounted value of payments made during the time step in question, and noting that floating payments are based on the short rate at each tree-node. Then (2), the option is valued similar to the approach for equity options: at nodes in the time-step corresponding to option maturity, value is based on moneynessMoneynessIn finance, moneyness is a measure of the degree to which a derivative is likely to have positive monetary value at its expiration, in the risk-neutral measure. It can be measured in percentage probability, or in standard deviations....
; at earlier nodes, it is the discounted expected value of the option at the up- and down-nodes in the later time step, and, depending on option styleOption styleIn finance, the style or family of an option is a general term denoting the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American options. These options - as well as others where the...
, of the swap value at the node. For both steps, the discounting is at the short rate at the tree-node in question. (Note that the Hull-White Model returns a Trinomial TreeTrinomial TreeThe Trinomial tree is a lattice based computational model used in financial mathematics to price options. It was developed by Phelim Boyle in 1986. It is an extension of the Binomial options pricing model, and is conceptually similar...
: the same logic is applied, although there are then three nodes in question at each point.)
- In valuing European swaptions using the Black modelBlack modelThe Black model is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing bond options, interest rate caps / floors, and swaptions...
, the underlierUnderlyingIn finance, the underlying of a derivative is an asset, basket of assets, index, or even another derivative, such that the cash flows of the derivative depend on the value of this underlying...
is treated as a forward contractForward contractIn finance, a forward contract or simply a forward is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed today. This is in contrast to a spot contract, which is an agreement to buy or sell an asset today. It costs nothing to enter a...
on a swap. Here, as mentioned, the forward priceForward priceThe forward price is the agreed upon price of an asset in a forward contract. Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, we can express the forward price in terms of the spot price and any dividends etc...
is the forward swap rate. The volatilityVolatility (finance)In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...
is typically "read-off" a two dimensional grid of at-the-money volatilities as observed from prices in the Interbank swaption market. On this grid, one axis is the time to expiration and the other is the length of the underlying swap. AdjustmentsGuesstimateGuesstimate is an informal English contraction of guess and estimate, first used by American statisticians in 1934 or 1935. It is defined as an estimate made without using adequate or complete information, or, more strongly, as an estimate arrived at by guesswork or conjecture...
may then be made for moneyness; see Implied volatility surface under Volatility smile.
First known swaption
The first known swaption was constructed and executed by William LawtonWilliam Lawton
William Lawton is Chairman of , an international merchant bank focused on sustainable community development through investments and trade in China, Southeast Asia and elsewhere. He is an expert in Asian investments and spoken on the topic at venues such as the Milken Conference. He worked closely...
in 1983. Lawton was the Head Trader for Fixed Income Derivatives at First Interstate Bank
First Interstate Bank (disambiguation)
First Interstate Bank may refer to one of the following:*First Interstate Bancorp of Los Angeles, California, which merged with Wells Fargo in 1996**Several buildings formerly named for the bank, now known as***Aon Center, Los Angeles, California...
in Los Angeles
Los Ángeles
Los Ángeles is the capital of the province of Biobío, in the commune of the same name, in Region VIII , in the center-south of Chile. It is located between the Laja and Biobío rivers. The population is 123,445 inhabitants...
at that time. Lawton worked with First Interstate's Treasury Options Desk to adapt the concept of an interest rate swap and an options contract. The swaption was for a period of one year. First Interstate, for a premium, sold a Los Angeles based savings and loan the right to enter into a five-year interest rate swap to pay fixed versus three-month Libor on a notional amount of $5 million [source needed]
External links
Theory- Longstaff, Francis A., Pedro Santa-Clara, and Eduardo S. Schwartz. The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence.
- Blanco, Carlos, Josh Gray and Marc Hazzard. Alternative Valuation Methods for Swaptions: The Devil is in the Details.
- Basic Fixed Income Derivative Hedging. Financial-edu.com.
- Martingales and Measures: Black's Model Dr. Jacqueline Henn-Overbeck, University of BaselUniversity of BaselThe University of Basel is located in Basel, Switzerland, and is considered to be one of leading universities in the country...
Tools
- Black-Swaption XLS Spreadsheet, thomasho.com