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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 In finance, an interest rate swap (IRS) is an interest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a "linear" IRD and one of the most liquid, benchmark products. It has associations with ...
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 Settlement may refer to: *Human settlement, a community where people live *Settlement (structural), the distortion or disruption of parts of a building * Closing (real estate), the final step in executing a real estate transaction *Settlement (fin ...
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 manage interest rate risk 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 Investment banking pertains to certain activities of a financial services company or a corporate division that consist in advisory-based financial transactions on behalf of individuals, corporations, and governments. Traditionally associated wit ...
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 medicines sold directly to a consumer without a requirement for a prescription from a healthcare professional, as opposed to prescription drugs, which may be supplied only to consumers possessing a valid prescr ...
(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 to
exotic option In finance, an exotic option is an option which has features making it more complex than commonly traded vanilla options. Like the more general exotic derivatives they may have several triggers relating to determination of payoff. An exotic op ...
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 the
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 To extract the forward rate, we ne ...
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) * Quantitative verse, a metrical system in poetry * Statistics, also known as quantitative analysis ...
s value swaptions by constructing complex lattice-based term structure and
short-rate model A short-rate model, in the context of interest rate derivatives, 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 Under a s ...
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 options, interest rate cap and floors, and swaptions. It ...
. 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 options, interest rate cap and floors, and swaptions. It ...
, 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 a forward contract. Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, the forward price can be expressed in t ...
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, the yield curve is a graph which depicts how the yields on debt instruments - such as bonds - vary as a function of their years remaining to maturity. Typically, the graph's horizontal or x-axis is a time line of months or ye ...
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, for a defined period of time, in exchange for a charge or fee.See "Time Value", "Discount", "Discount Yield", "Compound Interest", "Efficient ...
expected value 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, moneyness is the relative position of the current price (or future price) of an underlying asset (e.g., a stock) with respect to the strike price of a derivative, most commonly a call option or a put option. Moneyness is firstly a thr ...
; 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 style In finance, the style or family of an option is 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 (style) options. These optionsâ ...
, 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 Tree The 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. It can also ...
: the same logic is applied, although there are then three nodes in question at each point.) See .


See also

* Hedge (finance)


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 = 978-1-883249-25-0


External 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: ''Universitas Basiliensis'', German: ''Universität Basel'') is a university in Basel, Switzerland. Founded on 4 April 1460, it is Switzerland's oldest university and among the world's oldest surviving universit ...

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, a private research university based in New York City. I ...
Options (finance) Swaps (finance)