# swapbyzero

Price swap instrument from set of zero curves and price cross-currency swaps

## Syntax

## Description

`[`

prices
a swap instrument. You can use `Price`

,`SwapRate`

,`AI`

,`RecCF`

,`RecCFDates`

,`PayCF`

,`PayCFDates`

]
= swapbyzero(`RateSpec`

,`LegRate`

,`Settle`

,`Maturity`

)`swapbyzero`

to compute
prices of vanilla swaps, amortizing swaps, and forward swaps. All
inputs are either scalars or `NINST`

-by-`1`

vectors
unless otherwise specified. Any date can be a serial date number or
date character vector. An optional argument can be passed as an empty
matrix `[]`

.

`[`

prices
a swap instrument with additional options specified by one or more `Price`

,`SwapRate`

,`AI`

,`RecCF`

,`RecCFDates`

,`PayCF`

,`PayCFDates`

]
= swapbyzero(`RateSpec`

,`LegRate`

,`Settle`

,`Maturity`

,`Name,Value`

)`Name,Value`

pair
arguments. You can use `swapbyzero`

to compute prices
of vanilla swaps, amortizing swaps, forward swaps, and cross-currency
swaps. For more information on the name-value pairs for vanilla swaps,
amortizing swaps, and forward swaps, see Vanilla
Swaps, Amortizing Swaps, Forward Swaps.

Specifically, you can use name-value pairs for `FXRate`

, `ExchangeInitialPrincipal`

,
and `ExchangeMaturityPrincipal`

to compute the
price for cross-currency swaps. For more information on the name-value
pairs for cross-currency swaps, see Cross-Currency
Swaps.

## Examples

### Price an Interest-Rate Swap

Price an interest-rate swap with a fixed receiving leg and a floating paying leg. Payments are made once a year, and the notional principal amount is $100. The values for the remaining arguments are:

Coupon rate for fixed leg: 0.06 (6%)

Spread for floating leg: 20 basis points

Swap settlement date: Jan. 01, 2000

Swap maturity date: Jan. 01, 2003

Based on the information above, set the required arguments and build the `LegRate`

, `LegType`

, and `LegReset`

matrices:

Settle = '01-Jan-2000'; Maturity = '01-Jan-2003'; Basis = 0; Principal = 100; LegRate = [0.06 20]; % [CouponRate Spread] LegType = [1 0]; % [Fixed Float] LegReset = [1 1]; % Payments once per year

Load the file `deriv.mat`

, which provides `ZeroRateSpec`

, the interest-rate term structure needed to price the bond.

`load deriv.mat;`

Use `swapbyzero`

to compute the price of the swap.

Price = swapbyzero(ZeroRateSpec, LegRate, Settle, Maturity,... LegReset, Basis, Principal, LegType)

Price = 3.6923

Using the previous data, calculate the swap rate, which is the coupon rate for the fixed leg, such that the swap price at time = 0 is zero.

```
LegRate = [NaN 20];
[Price, SwapRate] = swapbyzero(ZeroRateSpec, LegRate, Settle,...
Maturity, LegReset, Basis, Principal, LegType)
```

Price = 0

SwapRate = 0.0466

In `swapbyzero`

, if `Settle`

is not on a reset date (and `'StartDate'`

is not specified), the effective date is assumed to be the previous reset date before `Settle`

in order to compute the accrued interest and dirty price. In this example, the effective date is ( `'15-Sep-2009'`

), which is the previous reset date before the ( `'08-Jun-2010'`

) `Settle`

date.

Use `swapbyzero`

with name-value pair arguments for `LegRate`

, `LegType`

, `LatestFloatingRate`

, `AdjustCashFlowsBasis`

, and `BusinessDayConvention`

to calculate output for `Price`

, `SwapRate`

, `AI`

, `RecCF`

, `RecCFDates`

, `PayCF`

, and `PayCFDates`

:

Settle = datenum('08-Jun-2010'); RateSpec = intenvset('Rates', [.005 .0075 .01 .014 .02 .025 .03]',... 'StartDates',Settle, 'EndDates',{'08-Dec-2010','08-Jun-2011',... '08-Jun-2012','08-Jun-2013','08-Jun-2015','08-Jun-2017','08-Jun-2020'}'); Maturity = datenum('15-Sep-2020'); LegRate = [.025 50]; LegType = [1 0]; % fixed/floating LatestFloatingRate = .005; [Price, SwapRate, AI, RecCF, RecCFDates, PayCF,PayCFDates] = ... swapbyzero(RateSpec, LegRate, Settle, Maturity,'LegType',LegType,... 'LatestFloatingRate',LatestFloatingRate,'AdjustCashFlowsBasis',true,... 'BusinessDayConvention','modifiedfollow')

Price = -6.7259

SwapRate = NaN

AI = 1.4575

`RecCF = `*1×12*
-1.8219 2.5000 2.5000 2.5137 2.4932 2.4932 2.5000 2.5000 2.5000 2.5137 2.4932 102.4932

`RecCFDates = `*1×12*
734297 734396 734761 735129 735493 735857 736222 736588 736953 737320 737684 738049

`PayCF = `*1×12*
-0.3644 0.5000 1.4048 1.9961 2.8379 3.2760 3.8218 4.1733 4.5164 4.4920 4.7950 104.6608

`PayCFDates = `*1×12*
734297 734396 734761 735129 735493 735857 736222 736588 736953 737320 737684 738049

### Price Swaps By Specifying Multiple Term Structures Using RateSpec

Price three swaps using two interest-rate curves. First, define the data for the interest-rate term structure:

StartDates = '01-May-2012'; EndDates = {'01-May-2013'; '01-May-2014';'01-May-2015';'01-May-2016'}; Rates = [[0.0356;0.041185;0.04489;0.047741],[0.0366;0.04218;0.04589;0.04974]];

Create the `RateSpec`

using `intenvset`

.

RateSpec = intenvset('Rates', Rates, 'StartDates',StartDates,... 'EndDates', EndDates, 'Compounding', 1)

`RateSpec = `*struct with fields:*
FinObj: 'RateSpec'
Compounding: 1
Disc: [4x2 double]
Rates: [4x2 double]
EndTimes: [4x1 double]
StartTimes: [4x1 double]
EndDates: [4x1 double]
StartDates: 734990
ValuationDate: 734990
Basis: 0
EndMonthRule: 1

Look at the `Rates`

for the two interest-rate curves.

RateSpec.Rates

`ans = `*4×2*
0.0356 0.0366
0.0412 0.0422
0.0449 0.0459
0.0477 0.0497

Define the swap instruments.

Settle = '01-May-2012'; Maturity = '01-May-2015'; LegRate = [0.06 10]; Principal = [100;50;100]; % Three notional amounts

Price three swaps using two curves.

`Price = swapbyzero(RateSpec, LegRate, Settle, Maturity, 'Principal', Principal)`

`Price = `*3×2*
3.9688 3.6869
1.9844 1.8434
3.9688 3.6869

### Price Swap By Specifying Multiple Term Structures Using a 1-by-2 `RateSpec`

Price a swap using two interest-rate curves. First, define data for the two interest-rate term structures:

StartDates = '01-May-2012'; EndDates = {'01-May-2013'; '01-May-2014';'01-May-2015';'01-May-2016'}; Rates1 = [0.0356;0.041185;0.04489;0.047741]; Rates2 = [0.0366;0.04218;0.04589;0.04974];

Create the `RateSpec`

using `intenvset`

.

RateSpecReceiving = intenvset('Rates', Rates1, 'StartDates',StartDates,... 'EndDates', EndDates, 'Compounding', 1); RateSpecPaying= intenvset('Rates', Rates2, 'StartDates',StartDates,... 'EndDates', EndDates, 'Compounding', 1); RateSpec=[RateSpecReceiving RateSpecPaying]

`RateSpec=`*1×2 struct array with fields:*
FinObj
Compounding
Disc
Rates
EndTimes
StartTimes
EndDates
StartDates
ValuationDate
Basis
EndMonthRule

Define the swap instruments.

Settle = '01-May-2012'; Maturity = '01-May-2015'; LegRate = [0.06 10]; Principal = [100;50;100];

Price three swaps using the two curves.

`Price = swapbyzero(RateSpec, LegRate, Settle, Maturity, 'Principal', Principal)`

`Price = `*3×1*
3.9693
1.9846
3.9693

### Compute a Forward Par Swap Rate

To compute a forward par swap rate, set the `StartDate`

parameter to a future date and set the fixed coupon rate in the `LegRate`

input to `NaN`

.

Define the zero curve data and build a zero curve using `IRDataCurve`

.

ZeroRates = [2.09 2.47 2.71 3.12 3.43 3.85 4.57]'/100; Settle = datenum('1-Jan-2012'); EndDates = datemnth(Settle,12*[1 2 3 5 7 10 20]'); Compounding = 1; ZeroCurve = IRDataCurve('Zero',Settle,EndDates,ZeroRates,'Compounding',Compounding)

ZeroCurve = Type: Zero Settle: 734869 (01-Jan-2012) Compounding: 1 Basis: 0 (actual/actual) InterpMethod: linear Dates: [7x1 double] Data: [7x1 double]

Create a `RateSpec`

structure using the `toRateSpec`

method.

RateSpec = ZeroCurve.toRateSpec(EndDates)

`RateSpec = `*struct with fields:*
FinObj: 'RateSpec'
Compounding: 1
Disc: [7x1 double]
Rates: [7x1 double]
EndTimes: [7x1 double]
StartTimes: [7x1 double]
EndDates: [7x1 double]
StartDates: 734869
ValuationDate: 734869
Basis: 0
EndMonthRule: 1

Compute the forward swap rate (the coupon rate for the fixed leg), such that the forward swap price at time = `0`

is zero. The forward swap starts in a month (1-Feb-2012) and matures in 10 years (1-Feb-2022).

StartDate = datenum('1-Feb-2012'); Maturity = datenum('1-Feb-2022'); LegRate = [NaN 0]; [Price, SwapRate] = swapbyzero(RateSpec, LegRate, Settle, Maturity,... 'StartDate', StartDate)

Price = 0

SwapRate = 0.0378

### Compute a Forward Swap Rate Using the Optional Input `BusinessDayConvention`

The `swapbyzero`

function generates the cash flow dates based on the `Settle`

and `Maturity`

dates, while using the `Maturity`

date as the "anchor" date from which to count backwards in regular intervals. By default, `swapbyzero`

does not distinguish non-business days from business days. To make `swapbyzero`

move non-business days to the following business days, you can you can set the optional name-value input argument `BusinessDayConvention`

with a value of `follow`

.

Define the zero curve data and build a zero curve using `IRDataCurve`

.

ZeroRates = [2.09 2.47 2.71 3.12 3.43 3.85 4.57]'/100; Settle = datenum('5-Jan-2012'); EndDates = datemnth(Settle,12*[1 2 3 5 7 10 20]'); Compounding = 1; ZeroCurve = IRDataCurve('Zero',Settle,EndDates,ZeroRates,'Compounding',Compounding); RateSpec = ZeroCurve.toRateSpec(EndDates); StartDate = datenum('5-Feb-2012'); Maturity = datenum('5-Feb-2022'); LegRate = [NaN 0];

To demonstrate the optional input `BusinessDayConvention`

, `swapbyzero`

is first used without and then with the optional name-value input argument `BusinessDayConvention`

. Notice that when using `BusinessDayConvention`

, all days are business days.

[Price1,SwapRate1,~,~,RecCFDates1,~,PayCFDates1] = swapbyzero(RateSpec,LegRate,Settle,Maturity,... 'StartDate',StartDate); datestr(RecCFDates1)

`ans = `*11x11 char array*
'05-Jan-2012'
'05-Feb-2013'
'05-Feb-2014'
'05-Feb-2015'
'05-Feb-2016'
'05-Feb-2017'
'05-Feb-2018'
'05-Feb-2019'
'05-Feb-2020'
'05-Feb-2021'
'05-Feb-2022'

isbusday(RecCFDates1)

`ans = `*11x1 logical array*
1
1
1
1
1
0
1
1
1
1
⋮

[Price2,SwapRate2,~,~,RecCFDates2,~,PayCFDates2] = swapbyzero(RateSpec,LegRate,Settle,Maturity,... 'StartDate',StartDate,'BusinessDayConvention','follow'); datestr(RecCFDates2)

`ans = `*12x11 char array*
'05-Jan-2012'
'06-Feb-2012'
'05-Feb-2013'
'05-Feb-2014'
'05-Feb-2015'
'05-Feb-2016'
'06-Feb-2017'
'05-Feb-2018'
'05-Feb-2019'
'05-Feb-2020'
'05-Feb-2021'
'07-Feb-2022'

isbusday(RecCFDates2)

`ans = `*12x1 logical array*
1
1
1
1
1
1
1
1
1
1
⋮

### Price an Amortizing Swap

Price an amortizing swap using the `Principal`

input argument to define the amortization schedule.

Create the `RateSpec`

.

Rates = 0.035; ValuationDate = '1-Jan-2011'; StartDates = ValuationDate; EndDates = '1-Jan-2017'; Compounding = 1; RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,... 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding);

Create the swap instrument using the following data:

Settle ='1-Jan-2011'; Maturity = '1-Jan-2017'; LegRate = [0.04 10];

Define the swap amortizing schedule.

Principal ={{'1-Jan-2013' 100;'1-Jan-2014' 80;'1-Jan-2015' 60;'1-Jan-2016' 40; '1-Jan-2017' 20}};

Compute the price of the amortizing swap.

`Price = swapbyzero(RateSpec, LegRate, Settle, Maturity, 'Principal' , Principal)`

Price = 1.4574

### Price a Forward Swap

Price a forward swap using the `StartDate`

input argument to define the future starting date of the swap.

Create the `RateSpec`

.

Rates = 0.0325; ValuationDate = '1-Jan-2012'; StartDates = ValuationDate; EndDates = '1-Jan-2018'; Compounding = 1; RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,... 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)

`RateSpec = `*struct with fields:*
FinObj: 'RateSpec'
Compounding: 1
Disc: 0.8254
Rates: 0.0325
EndTimes: 6
StartTimes: 0
EndDates: 737061
StartDates: 734869
ValuationDate: 734869
Basis: 0
EndMonthRule: 1

Compute the price of a forward swap that starts in a year (Jan 1, 2013) and matures in three years with a forward swap rate of 4.27%.

Settle ='1-Jan-2012'; StartDate = '1-Jan-2013'; Maturity = '1-Jan-2016'; LegRate = [0.0427 10]; Price = swapbyzero(RateSpec, LegRate, Settle, Maturity, 'StartDate' , StartDate)

Price = 2.5083

Using the previous data, compute the forward swap rate, the coupon rate for the fixed leg, such that the forward swap price at time = 0 is zero.

LegRate = [NaN 10]; [Price, SwapRate] = swapbyzero(RateSpec, LegRate, Settle, Maturity,... 'StartDate' , StartDate)

Price = 0

SwapRate = 0.0335

### Specify the Rate at the Instrument’s Starting Date When It Cannot Be Obtained from the `RateSpec`

If `Settle`

is not on a reset
date of a floating-rate note, `swapbyzero`

attempts
to obtain the latest floating rate before `Settle`

from `RateSpec`

or
the `LatestFloatingRate`

parameter. When the reset
date for this rate is out of the range of `RateSpec`

(and `LatestFloatingRate`

is
not specified), `swapbyzero`

fails to obtain the
rate for that date and generates an error. This example shows how
to use the `LatestFloatingRate`

input parameter to
avoid the error.

Create the error condition when a swap instrument’s `StartDate`

cannot
be determined from the `RateSpec`

.

Settle = '01-Jan-2000'; Maturity = '01-Dec-2003'; Basis = 0; Principal = 100; LegRate = [0.06 20]; % [CouponRate Spread] LegType = [1 0]; % [Fixed Float] LegReset = [1 1]; % Payments once per year load deriv.mat; Price = swapbyzero(ZeroRateSpec,LegRate,Settle,Maturity,... 'LegReset',LegReset,'Basis',Basis,'Principal',Principal, ... 'LegType',LegType)

Error using floatbyzero (line 256) The rate at the instrument starting date cannot be obtained from RateSpec. Its reset date (01-Dec-1999) is out of the range of dates contained in RateSpec. This rate is required to calculate cash flows at the instrument starting date. Consider specifying this rate with the 'LatestFloatingRate' input parameter. Error in swapbyzero (line 289) [FloatFullPrice, FloatPrice,FloatCF,FloatCFDates] = floatbyzero(FloatRateSpec, Spreads, Settle,...

Here, the reset date for the rate at `Settle`

was `01-Dec-1999`

,
which was earlier than the valuation date of `ZeroRateSpec`

(`01-Jan-2000`

).
This error can be avoided by specifying the rate at the swap instrument’s
starting date using the `LatestFloatingRate`

input
parameter.

Define `LatestFloatingRate`

and calculate
the floating-rate price.

Price = swapbyzero(ZeroRateSpec,LegRate,Settle,Maturity,... 'LegReset',LegReset,'Basis',Basis,'Principal',Principal, ... 'LegType',LegType,'LatestFloatingRate',0.03)

Price = 4.7594

### Price a Swap Using a Different Curve to Generate the Cash Flows of the Floating Leg

Define the OIS and Libor rates.

```
Settle = datenum('15-Mar-2013');
CurveDates = daysadd(Settle,360*[1/12 2/12 3/12 6/12 1 2 3 4 5 7 10],1);
OISRates = [.0018 .0019 .0021 .0023 .0031 .006 .011 .017 .021 .026 .03]';
LiborRates = [.0045 .0047 .005 .0055 .0075 .011 .016 .022 .026 .030 .0348]';
```

Plot the dual curves.

figure,plot(CurveDates,OISRates,'r');hold on;plot(CurveDates,LiborRates,'b') datetick legend({'OIS Curve', 'Libor Curve'})

Create an associated `RateSpec`

for the OIS and Libor curves.

OISCurve = intenvset('Rates',OISRates,'StartDate',Settle,'EndDates',CurveDates); LiborCurve = intenvset('Rates',LiborRates,'StartDate',Settle,'EndDates',CurveDates);

Define the swap.

Maturity = datenum('15-Mar-2018'); % Five year swap FloatSpread = 0; FixedRate = .025; LegRate = [FixedRate FloatSpread];

Compute the price of the swap instrument. The `LiborCurve`

term structure will be used to generate the cash flows of the floating leg. The `OISCurve`

term structure will be used for discounting the cash flows.

Price = swapbyzero(OISCurve, LegRate, Settle,... Maturity,'ProjectionCurve',LiborCurve)

Price = -0.3697

Compare results when the term structure `OISCurve`

is used both for discounting and also generating the cash flows of the floating leg.

PriceSwap = swapbyzero(OISCurve, LegRate, Settle, Maturity)

PriceSwap = 2.0517

### Price a Fixed-Fixed Currency Swap

Price an existing cross currency swap that receives a fixed rate of JPY and pays a fixed rate of USD at an annual frequency.

Settle = datenum('15-Aug-2015'); Maturity = datenum('15-Aug-2018'); Reset = 1; LegType = [1 1]; % Fixed-Fixed r_USD = .09; r_JPY = .04; FixedRate_USD = .08; FixedRate_JPY = .05; Principal_USD = 10000000; Principal_JPY = 1200000000; S = 1/110; RateSpec_USD = intenvset('StartDate',Settle,'EndDate', Maturity,'Rates',r_USD,'Compounding',-1); RateSpec_JPY = intenvset('StartDate',Settle,'EndDate', Maturity,'Rates', r_JPY,'Compounding',-1); Price = swapbyzero([RateSpec_JPY RateSpec_USD], [FixedRate_JPY FixedRate_USD],... Settle, Maturity,'Principal',[Principal_JPY Principal_USD],'FXRate',[S 1], 'LegType',LegType)

Price = 1.5430e+06

### Price a Float-Float Currency Swap

Price a new swap where you pay a EUR float and receive a USD float.

Settle = datenum('22-Dec-2015'); Maturity = datenum('15-Aug-2018'); LegRate = [0 -50/10000]; LegType = [0 0]; % Float Float LegReset = [4 4]; FXRate = 1.1; Notional = [10000000 8000000]; USD_Dates = datemnth(Settle,[1 3 6 12*[1 2 3 5 7 10 20 30]]'); USD_Zero = [0.03 0.06 0.08 0.13 0.36 0.76 1.63 2.29 2.88 3.64 3.89]'/100; Curve_USD = intenvset('StartDate',Settle,'EndDates',USD_Dates,'Rates',USD_Zero); EUR_Dates = datemnth(Settle,[3 6 12*[1 2 3 5 7 10 20 30]]'); EUR_Zero = [0.017 0.033 0.088 .27 .512 1.056 1.573 2.183 2.898 2.797]'/100; Curve_EUR = intenvset('StartDate',Settle,'EndDates',EUR_Dates,'Rates',EUR_Zero); Price = swapbyzero([Curve_USD Curve_EUR], ... LegRate, Settle, Maturity,'LegType',LegType,'LegReset',LegReset,'Principal',Notional,... 'FXRate',[1 FXRate],'ExchangeInitialPrincipal',false)

Price = 1.2002e+06

## Input Arguments

`RateSpec`

— Interest-rate structure

structure

Interest-rate structure, specified using `intenvset`

to create a `RateSpec`

.

`RateSpec`

can also be a `1`

-by-`2`

input
variable of `RateSpec`

s, with the second `RateSpec`

structure
containing one or more discount curves for the paying leg. If only
one `RateSpec`

structure is specified, then this `RateSpec`

is
used to discount both legs.

**Data Types: **`struct`

`LegRate`

— Leg rate

matrix

Leg rate, specified as a `NINST`

-by-`2`

matrix,
with each row defined as one of the following:

`[CouponRate Spread]`

(fixed-float)`[Spread CouponRate]`

(float-fixed)`[CouponRate CouponRate]`

(fixed-fixed)`[Spread Spread]`

(float-float)

`CouponRate`

is the decimal annual rate.
`Spread`

is the number of basis points over the reference rate. The
first column represents the receiving leg, while the second column represents the
paying leg.

**Data Types: **`double`

`Settle`

— Settlement date

serial date number | character vector | cell array of character vectors

Settlement date, specified either as a scalar or `NINST`

-by-`1`

vector
of serial date numbers or date character vectors of the same value
which represent the settlement date for each swap. `Settle`

must
be earlier than `Maturity`

.

**Data Types: **`char`

| `cell`

| `double`

`Maturity`

— Maturity date

serial date number | character vector | cell array of character vectors

Maturity date, specified as a `NINST`

-by-`1`

vector
of serial date numbers or date character vectors representing the
maturity date for each swap.

**Data Types: **`char`

| `cell`

| `double`

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

**Example: **```
[Price,SwapRate,AI,RecCF,RecCFDates,PayCF,PayCFDates] =
swapbyzero(RateSpec,LegRate,Settle,
```

Maturity,'LegType',LegType,'LatestFloatingRate',LatestFloatingRate,'AdjustCashFlowsBasis',true,

'BusinessDayConvention','modifiedfollow')

**Vanilla Swaps, Amortizing Swaps, Forward Swaps**

`LegReset`

— Reset frequency per year for each swap

`[1 1]`

(default) | vector

Reset frequency per year for each swap, specified as the comma-separated pair
consisting of `'LegReset'`

and a
`NINST`

-by-`2`

vector.

**Data Types: **`double`

`Basis`

— Day-count basis of instrument

`0`

(actual/actual) (default) | integer from `0`

to `13`

Day-count basis representing the basis for each leg, specified as the
comma-separated pair consisting of `'Basis'`

and a
`NINST`

-by-`1`

array (or
`NINST`

-by-`2`

if `Basis`

is
different for each leg).

0 = actual/actual

1 = 30/360 (SIA)

2 = actual/360

3 = actual/365

4 = 30/360 (PSA)

5 = 30/360 (ISDA)

6 = 30/360 (European)

7 = actual/365 (Japanese)

8 = actual/actual (ICMA)

9 = actual/360 (ICMA)

10 = actual/365 (ICMA)

11 = 30/360E (ICMA)

12 = actual/365 (ISDA)

13 = BUS/252

For more information, see Basis.

**Data Types: **`double`

`Principal`

— Notional principal amounts or principal value schedules

`100`

(default) | vector or cell array

Notional principal amounts or principal value schedules, specified as the
comma-separated pair consisting of `'Principal'`

and a vector or cell
array.

`Principal`

accepts a
`NINST`

-by-`1`

vector or
`NINST`

-by-`1`

cell array (or
`NINST`

-by-`2`

if `Principal`

is different for each leg) of the notional principal amounts or principal value
schedules. For schedules, each element of the cell array is a
`NumDates`

-by-`2`

array where the first column
is dates and the second column is its associated notional principal value. The date
indicates the last day that the principal value is valid.

**Data Types: **`cell`

| `double`

`LegType`

— Leg type

`[1 0]`

for each instrument (default) | matrix with values `[1 1]`

(fixed-fixed), ```
[1
0]
```

(fixed-float), `[0 1]`

(float-fixed), or ```
[0
0]
```

(float-float)

Leg type, specified as the comma-separated pair consisting of
`'LegType'`

and a `NINST`

-by-`2`

matrix with values `[1 1]`

(fixed-fixed), `[1 0]`

(fixed-float), `[0 1]`

(float-fixed), or `[0 0]`

(float-float). Each row represents an instrument. Each column indicates if the
corresponding leg is fixed (`1`

) or floating (`0`

).
This matrix defines the interpretation of the values entered in
`LegRate`

. `LegType`

allows ```
[1
1]
```

(fixed-fixed), `[1 0]`

(fixed-float), ```
[0
1]
```

(float-fixed), or `[0 0]`

(float-float) swaps

**Data Types: **`double`

`EndMonthRule`

— End-of-month rule flag for generating dates when `Maturity`

is end-of-month date for month having 30 or fewer days

`1`

(in effect) (default) | nonnegative integer `[0,1]`

End-of-month rule flag for generating dates when `Maturity`

is
an end-of-month date for a month having 30 or fewer days, specified as the
comma-separated pair consisting of `'EndMonthRule'`

and a nonnegative
integer [`0`

, `1`

] using a
`NINST`

-by-`1`

(or
`NINST`

-by-`2`

if `EndMonthRule`

is different for each leg).

`0`

= Ignore rule, meaning that a payment date is always the same numerical day of the month.`1`

= Set rule on, meaning that a payment date is always the last actual day of the month.

**Data Types: **`logical`

`AdjustCashFlowsBasis`

— Flag to adjust cash flows based on actual period day count

`false`

(default) | value of `0`

(false) or `1`

(true)

Flag to adjust cash flows based on actual period day count, specified as the
comma-separated pair consisting of `'AdjustCashFlowsBasis'`

and a
`NINST`

-by-`1`

(or
`NINST`

-by-`2`

if
`AdjustCashFlowsBasis`

is different for each leg) of logicals with
values of `0`

(false) or `1`

(true).

**Data Types: **`logical`

`BusinessDayConvention`

— Business day conventions

`actual`

(default) | character vector | cell array of character vectors

Business day conventions, specified as the comma-separated pair consisting of
`'BusinessDayConvention'`

and a character vector or a
`N`

-by-`1`

(or
`NINST`

-by-`2`

if
`BusinessDayConvention`

is different for each leg) cell array of
character vectors of business day conventions. The selection for business day
convention determines how non-business days are treated. Non-business days are defined
as weekends plus any other date that businesses are not open (e.g. statutory
holidays). Values are:

`actual`

— Non-business days are effectively ignored. Cash flows that fall on non-business days are assumed to be distributed on the actual date.`follow`

— Cash flows that fall on a non-business day are assumed to be distributed on the following business day.`modifiedfollow`

— Cash flows that fall on a non-business day are assumed to be distributed on the following business day. However if the following business day is in a different month, the previous business day is adopted instead.`previous`

— Cash flows that fall on a non-business day are assumed to be distributed on the previous business day.`modifiedprevious`

— Cash flows that fall on a non-business day are assumed to be distributed on the previous business day. However if the previous business day is in a different month, the following business day is adopted instead.

**Data Types: **`char`

| `cell`

`Holidays`

— Holidays used in computing business days

if not specified, the default is to use
`holidays.m`

(default) | MATLAB^{®} date numbers

Holidays used in computing business days, specified as the comma-separated pair
consisting of `'Holidays'`

and MATLAB date numbers using a
`NHolidays`

-by-`1`

vector.

**Data Types: **`double`

`StartDate`

— Dates when swaps actually start

If not specified, date is `Settle`

(default) | serial date number | character vector | cell array of character vectors

Dates when the swaps actually start, specified as the comma-separated pair
consisting of `'StartDate'`

and a
`NINST`

-by-`1`

vector of serial date numbers,
character vectors, or cell array of character vectors.

**Data Types: **`char`

| `cell`

| `double`

`LatestFloatingRate`

— Rate for the next floating payment

If not specified, then `RateSpec`

must contain
this information (default) | scalar numeric

Rate for the next floating payment, set at the last reset date, specified as the
comma-separated pair consisting of `'LatestFloatingRate'`

and a
scalar numeric value.

`LatestFloatingRate`

accepts a Rate for the next floating
payment, set at the last reset date. `LatestFloatingRate`

is a
`NINST`

-by-`1`

(or
`NINST`

-by-`2`

if
`LatestFloatingRate`

is different for each leg).

**Data Types: **`double`

`ProjectionCurve`

— Rate curve used in generating cash flows for the floating leg of the swap

if `ProjectionCurve`

is not specified, then
`RateSpec`

is used both for discounting and generating cash flows
for the floating leg (default) | `RateSpec`

or vector

Rate curve used in generating cash flows for the floating leg of the swap,
specified as the comma-separated pair consisting of
`'ProjectionCurve'`

and a `RateSpec`

.

If specifying a fixed-float or a float-fixed swap, the
`ProjectionCurve`

rate curve is used in generating cash flows for
the floating leg of the swap. This structure must be created using `intenvset`

.

If specifying a fixed-fixed or a float-float swap, then
`ProjectionCurve`

is
`NINST`

-by-`2`

vector because each floating leg
could have a different projection curve.

**Data Types: **`struct`

**Cross-Currency Swaps**

`FXRate`

— Foreign exchange (FX) rate applied to cash flows

if not specified, both legs of `swapbyzero`

are
in same currency (default) | array

Foreign exchange (FX) rate applied to cash flows, specified as the
comma-separated pair consisting of `'FXRate'`

and a
`NINST`

-by-`2`

array of doubles. Since the foreign
exchange rate could be applied to either the payer or receiver leg, there are 2
columns in the input array and you must specify which leg has the foreign
currency.

**Data Types: **`double`

`ExchangeInitialPrincipal`

— Flag to indicate if initial `Principal`

is exchanged

`0`

(false) (default) | array

Flag to indicate if initial `Principal`

is exchanged,
specified as the comma-separated pair consisting of
`'ExchangeInitialPrincipal'`

and a
`NINST`

-by-`1`

array of logicals.

**Data Types: **`logical`

`ExchangeMaturityPrincipal`

— Flag to indicate if `Principal`

exchanged at `Maturity`

`1`

(true) (default) | array

Flag to indicate if `Principal`

is exchanged at
`Maturity`

, specified as the comma-separated pair consisting of
`'ExchangeMaturityPrincipal'`

and a
`NINST`

-by-`1`

array of logicals. While in
practice most single currency swaps do not exchange principal at maturity, the default
is true to maintain backward compatibility.

**Data Types: **`logical`

## Output Arguments

`Price`

— Swap prices

matrix

Swap prices, returned as the number of instruments (`NINST`

)
by number of curves (`NUMCURVES`

) matrix. Each column
arises from one of the zero curves. `Price`

output
is the dirty price. To compute the clean price, subtract the accrued
interest (`AI`

) from the dirty price.

`SwapRate`

— Rates applicable to fixed leg

matrix

Rates applicable to the fixed leg, returned as a `NINST`

-by-`NUMCURVES`

matrix
of rates applicable to the fixed leg such that the swaps’ values
are zero at time 0. This rate is used in calculating the swaps’
prices when the rate specified for the fixed leg in `LegRate`

is `NaN`

.
The `SwapRate`

output is padded with `NaN`

for
those instruments in which `CouponRate`

is not set
to `NaN`

.

`AI`

— Accrued interest

matrix

Accrued interest, returned as a `NINST`

-by-`NUMCURVES`

matrix.

`RecCF`

— Cash flows for receiving leg

matrix

Cash flows for the receiving leg, returned as a `NINST`

-by-`NUMCURVES`

matrix.

**Note**

If there is more than one curve specified in the `RateSpec`

input,
then the first `NCURVES`

row corresponds to the first
swap, the second `NCURVES`

row correspond to the
second swap, and so on.

`RecCFDates`

— Payment dates for receiving leg

matrix

Payment dates for the receiving leg, returned as an `NINST`

-by-`NUMCURVES`

matrix.

`PayCF`

— Cash flows for paying leg

matrix

Cash flows for the paying leg, returned as an `NINST`

-by-`NUMCURVES`

matrix.

`PayCFDates`

— Payment dates for paying leg

matrix

Payment dates for the paying leg, returned as an `NINST`

-by-`NUMCURVES`

matrix.

## More About

### Amortizing Swap

In an amortizing swap, the notional principal decreases periodically because it is tied to an underlying financial instrument with a declining (amortizing) principal balance, such as a mortgage.

### Forward Swap

Agreement to enter into an interest-rate swap arrangement on a fixed date in future.

### Cross-currency Swap

Swaps where the payment legs of the swap are denominated in different currencies.

One difference between cross-currency swaps and standard swaps is that an exchange of principal may occur at the beginning and/or end of the swap. The exchange of initial principal will only come into play in pricing a cross-currency swap at inception (in other words, pricing an existing cross-currency swap will occur after this cash flow has happened). Furthermore, these exchanges of principal typically do not affect the value of the swap (since the principal values of the two legs are chosen based on the currency exchange rate) but affect the cash flows for each leg.

## References

[1] Hull, J. *Options, Futures and Other Derivatives* Fourth
Edition. Prentice Hall, 2000.

## Version History

**Introduced before R2006a**

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