A swaption is an

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,

Black-Scholes and binomial valuation of swaptions

(Advanced Fixed Income Analytics 4:5), Prof. D. Backus and Prof. S. Zin,

option
Option or Options may refer to:
Computing
*Option key, a key on Apple computer keyboards
*Option type, a polymorphic data type in programming languages
*Command-line option, an optional parameter to a command
*OPTIONS, an Hypertext Transfer Prot ...

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
In finance
Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and investments. Savers and investors have money available ...

s.
Types of swaptions

There are two types of swaption contracts (analogous to put and call options): *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. In addition, a "straddle" refers to a combination of a receiver and a payer option on the same underlying swap. The buyer and seller of the swaption agree on: *The premium (price) of the swaption *Length of the option period (which usually ends two business days prior to the start date of the underlying swap), *The terms of the underlying swap, including: **Notional amount (with amortization amounts, if any) **The fixed rate (which equals the strike of the swaption) and payment frequency for the fixed leg **The frequency of observation for the floating leg of the swap (for example, 3 month Libor paid quarterly) There are two possible settlement conventions. Swaptions can be settled physically (i.e., at expiry the swap is entered between the two parties) or cash-settled, where the value of the swap at expiry is paid according to a market-standard formula.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 manageinterest rate risk
Interest rate risk is the risk
In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, we ...

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. Investment banks
An investment bank is a financial services
Financial services are the Service (economics), economic services provided by the finance industry, which encompasses a broad range of businesses that manage money, including credit unions, banks, credit ...

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 and risk-manage 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 primarily over-the-counter
Over-the-counter (OTC) drugs are medicine
Medicine is the Art (skill), art, science, and Praxis (process) , practice of caring for a patient and managing the diagnosis, prognosis, Preventive medicine, prevention, therapy, treatment or Palliat ...

(OTC), i.e., not cleared or traded on an exchange. Legally, a swaption is a contract granting a party the right to enter an agreement with another counterparty to exchange the required payments. The owner ("buyer") of the swaption is exposed to a failure by the "seller" to enter the swap upon expiry (or to pay the agreed payoff in the case of a cash-settled swaption). Often this exposure is mitigated through the use of collateral agreements whereby variation margin is posted to cover the anticipated future exposure.
Swaption exercise styles

There are three main styles that define the exercise of the Swaption: *European swaption, in which the owner is allowed to enter the swap only at the start of the swap. These are the standard in the marketplace. *Bermudan swaption, in which the owner is allowed to enter the swap on multiple specified dates, typically coupon dates during the life of the underlying swap. *American swaption, in which the owner is allowed to enter the swap on any day that falls within a range of two dates. Exotic desks may be willing to create customised types of Swaptions, analogous toexotic option
In finance
Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and investments. Savers and investors have money available ...

s. These can involve bespoke exercise rules, or a non-constant swap notional.
Valuation

The valuation of swaptions is complicated in that the at-the-money level is the forward swap rate, being theforward 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
To extract the forward rate, we n ...

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
Quantitative may refer to:
* Quantitative research, scientific investigation of quantitative properties
* Quantitative analysis (disambiguation)
* Meter (poetry), Quantitative verse, a metrical system in poetry
* Statistics, also known as quantit ...

s value swaptions by constructing complex lattice-based term structure
In finance, the yield curve is a curve showing several Yield to maturity, yields to maturity or interest rates across different contract lengths (2 month, 2 year, 20 year, etc. ...) for a similar debt contract. The curve shows the relatio ...

and short-rate modelA short-rate model, in the context of interest rate derivatives, is a mathematical model
A mathematical model is a description of a system
A system is a group of Interaction, interacting or interrelated elements that act according to a set of ...

s that describe the movement of interest rates over time. However, a standard practice, particularly amongst traders, to whom ''speed'' of calculation is more important, is to value European swaptions using the Black model
The Black model (sometimes known as the Black-76 model) is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing options on future contracts, bond option
In finance
Finance is the study of financial i ...

. For American- and Bermudan- styled options, where exercise is permitted prior to maturity, only the lattice based approach is applicable.
*In valuing European swaptions using the Black model
The Black model (sometimes known as the Black-76 model) is a variant of the Black–Scholes option pricing model. Its primary applications are for pricing options on future contracts, bond option
In finance
Finance is the study of financial i ...

, the underlier is treated as a forward contract
In 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 on at the time of conclusion of the contract, making it a type of derivat ...

on a swap. Here, as mentioned, the forward price
The forward price (or sometimes forward rate) is the agreed upon price of an asset
In financial accountancy, financial accounting, an asset is any resource owned or controlled by a business or an economic entity. It is anything (tangible or inta ...

is the forward swap rate. The volatility 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. Adjustments may then be made for moneyness; see Implied volatility surface under Volatility smile.
*To use the lattice based approach, the analyst constructs a "tree" of short rates—a zeroeth step—consistent with today's yield curve
In finance
Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and investments. Savers and investors have money avai ...

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 Ho–Lee, 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 discounted
Discounting is a financial mechanism in which a debtor obtains the right to delay payments to a creditor
A creditor or lender is a party (e.g., person, organization, company, or government) that has a claim on the services of a second party. ...

expected value
In probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by exp ...

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 moneyness
In finance
Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of money and investments. Savers and investors have money available ...

; 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 styleIn finance, the style or family of an option (finance), option is the class into which the option falls, usually defined by the dates on which the option may be Exercise (options), exercised. The vast majority of options are either European or Ameri ...

, 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 TreeThe trinomial tree is a lattice-based computational model used in financial mathematicsMathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of fi ...

: the same logic is applied, although there are then three nodes in question at each point.) See .
See also

*Hedge (finance)
A hedge is an investment position intended to offset potential losses or gains that may be incurred by a companion investment. A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insuran ...

Notes

References

* * *{{cite book , title = Valuation of fixed income securities and derivatives , author = Frank Fabozzi , author-link = Frank Fabozzi , publisher = John Wiley, year = 1998, edition = 3rd, isbn = 978-1-883249-25-0External links

*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 Basel
The University of Basel (Latin
Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of ...

Black-Scholes and binomial valuation of swaptions

(Advanced Fixed Income Analytics 4:5), Prof. D. Backus and Prof. S. Zin,

New York University Stern School of Business
The New York University Leonard N. Stern School of Business (commonly referred to as NYU Stern, The Stern School of Business, or simply Stern) is the business school of New York University
New York University (NYU) is a private research u ...

Options (finance)
Swaps (finance)