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. An payer swaption is also called a right-to-pay swaption that allows its holder to exercise into a swap where the holder pays fixed rates and receives floating rates, while a receiver swaption is also called right-to-receive swaption that allows its holders to exercise into a 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. This presentation gives an overview of swaption product and valuation. 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. A payer swaption is also called a right-to-pay swaption that allows its holder to exercise into a 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 a 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.
Keywords
Swaption, interest rate swap, payer swaption, receiver swaption, financial product, valuation model.
Swaption Introduction
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.
A payer swaption is also called a right-to-pay swaption that allows its holder to exercise into a 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 a 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.
Use of Swaption
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.
Swaption Payoff
For a payer swaption, the payoff at payment date T is given by
〖Payff〗_payer=max(0,NA(S_T-S_0) (1) where N- the notional; A – the annuity or forward basis point value S_0 – the fixed rate or contract swap rate at inception S_T – the swap rate at time T. From a receiver swaption, , the payoff at payment date T is given by 〖Payff〗_payer=max(0,NA(S_0-S_T) (2)
Valuation
The present value of a payer swaption is given by
〖PV〗payer (t)=NA[SΦ(d_1 )-KΦ(d_2)] (1)
where
t – valuation date
N – notational principal amount
A=∑(i=1)^n▒〖τ_i D_i 〗 – annuity factor or forward basis point value
S=[D_1-D_n ]⁄A - forward swap rate
- the cumulative standard normal distribution function i – ith cash flow (swaplet) of the underlying swap from 1 to n τ_i=τ(T_(i-1),T_i) – the accrual period ( , ) of the ith cash flow. D_i=D(t,T_i) – the discount factor The present value of a receiver swaption can be expressed as
〖PV〗_payer (t)=NA[KΦ(〖-d〗_2 )-SΦ(〖-d〗_1 )] (2)
where all notations are the same as (1)
Practical notes
A swaption contract contains terms and conditions of the swaption and the underlying swap. For example, it specifies two maturities: swaption maturity and underlying swap maturity.
The valuation model for pricing a swaption is Black formula that assumes the underlying swap rate follows a log-normal process.
First, one needs to generate the cash flows of the underlying 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
Any compounded interest zero rate 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.
The other key for accurately pricing an outstanding swaption is to construct an arbitrage-free volatility surface. Unlike a cap/floor volatility surface that is 3 dimensional (maturity – strike – volatility), a swaption volatility surface is 4 dimensional (swaption maturity – underlying swap tenor – strike – volatility).
A Real World Example
Swaption Specification Underlying Swap Specification Buy Sell Buy Leg 1 Specification Leg 2 Specification Pay Receive Ray Currency USD Currency USD Notification Lag 2 Day Count dc30360 Day Count dcAct360 Settlement Cash Leg Type Fixed Leg Type Float Exercise Type Call Notional 25000000 Notional 25000000 Notification Date 4/30/2020 Pay Receive Pay Pay Receive Receive Settlement Date 5/5/2020 Payment Freq 6 Payment Freq 3 Forward Premium Amount 3375000 Start Date 5/5/2020 Start Date 5/5/2020 Premium Pay Receive Pay End Date 5/5/2030 End Date 5/5/2030 Forward Premium Date 5/5/2020 Fixed Rate 0.02855 Spread 0 Index Specification Type LIBOR Tenor 3M Day Count dcAct360
Reference:
https://finpricing.com/lib/EqAutocallable.html
https://bitbucket.org/cmrm11/irswaption/downloads/IrSwaption-37.pdf