Swaption


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Swaption Valuation


FinPricing provides valuation models and tools for:

  • Swaption
  • Calculating Swaption Price Given Implied Volatility
  • Calculating Implied Volatility Given Swaption Price
  • Bermudan Swaption
  • Cancelable Swap
  • Equity-Linked Cancelable Swap (Yield Note)
  • Equity Participation Swap
  • Check FinPricing valuation models

An interest rate swaption or interest rate European swaption is an OTC option that grants its owner the right but not the obligation to enter an underlying interest rate swap. There are two types of swaptions: a payer swaption and a receiver swaption.


1. Swaption Introduction

There are two types of swaptions: a payer swaption and a receiver swaption. A payer swaption is also called a right-to-pay swaption that allows its holder to exercise into an interest rate swap where the holder pays fixed rates and receives floating rates. A receiver swaption is also called right-to-receive swaption that allows its holders to exercise into an interest rate swap where the holder receives fixed rates and pays floating rates. Swaptions provide clients with a guarantee that the fixed rate of interest they will pay at some of future time will not exceed certain level.

Market participants use swaptions to manage interest rate risk arising from their business. A firm might buy a payer swaption if it wants protection from rising interest rates. A corporation holding a mortgage portfolio might buy a receiver swaption to protect against decreasing interest rates that might lead to mortgage prepayment. A company believing that interest rates will not increase much might sell a payer swaption and earns the premium. An institution believing that interest rates will not decrease much might sell a receiver swaption and earns the premium.


2. Swaption Valuation

The present value of a payer swaption is given by

Payer swaption valuation in FinPricing

The present value of a receiver swaption can be expressed as

receiver swaption valuation in FinPricing

where all notations are the same as (1)

Practical Notes

  • A swaption contract contains terms and conditions of the swaption and the underlying interest rate swap. For example, it specifies two maturities: swaption maturity and underlying swap maturity/tenor.
  • The valuation model for pricing a swaption is the Black formula.
  • First, one needs to generate the cash flows of the underlying interest rate swap. The generation is based on the start time, end time and payment frequency of each leg, plus calendar (holidays), business convention (e.g., modified following, following, etc.) and whether sticky month end.
  • The accrual period is calculated according to the start date and end date of a cash flow plus day count convention
  • Then you need to construct interest zero curve by bootstrapping the most liquid interest rate instruments in the market. FinPricing provides useful tools to build various curves, such as swap curve, basis curve, OIS curve, bond curve, treasury curve, etc. Go to the list of the tools
  • Any compounded interest yield curves can be used to compute discount factor, of course the formulas will be slightly different. The most common used one is continuously compounded zero rates.
  • Another key for accurately pricing an outstanding swaption is to construct an arbitrage-free volatility surface. Unlike a cap implied volatility surface that is 3 dimensional (maturity – strike – volatility), a implied swaption volatility surface is 4 dimensional (swaption maturity – underlying swap tenor – strike – volatility).
  • FinPricing is using SABR model to contruct swaption implied volatility.  Go to the list of volatility construction tools
3. Related Topic: Interest Rate Swap

An interest rate swap is an agreement between two parties to exchange future interest rate payments over a set period of time. It consists of a series of payment periods, called swaplets. The most popular form of interest rate swaps is the vanilla swaps that involve the exchange of a fixed interest rate for a floating rate, or vice versa. There are two legs associated with each party: a fixed leg and a floating leg. Interest rate swaps are OTC derivatives that bear counterparty credit risk beside interest rate risk.

The present value of a fixed leg is given by

Pricing fixed leg of interest rate swap in FinPricing

The present value of a floating leg can be expressed as

Pricing floating leg of interest rate swap in FinPricing

The final present value of the swap is

Calculate interest rate swap MTM in FinPricing

Swap Rate and Swap Spread

A swap rate is the fixed rate that makes a given interest rate swap worth zero at inception.It can be easily derived from (1) and (2) as follows.

Compute swap rate in FinPricing

Swap spread is defined as the difference between a swap rate and the rate of an on-the-run treasury with the same maturity as the interest rate swap. The swap spread is the additional amount an investor would earn on an interest rate swap as compared to a risk-free fixed-rate investment.

Final practical notes

  • Interest rate swaps are the most popular OTC derivatives. Most of them are either collateralized or cleared in the market. Therefore, pricing model should use OIS discounting to account for collateralization.
  • Some dealers take bid-offer spreads into account. In this case, one should use bid curve constructed from bid quotes for forwarding and offer curve built from offer quotes for discounting.

References

You can find more details at Interest Rate Swap