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swapbyzero

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

Syntax

  • [Price,SwapRate,AI,RecCF,RecCFDates,PayCF,PayCFDates] =
    swapbyzero(RateSpec,LegRate,Settle,Maturity)
    example
  • [Price,SwapRate,AI,RecCF,RecCFDates,PayCF,PayCFDates] =
    swapbyzero(RateSpec,LegRate,Settle,Maturity,Name,Value)
    example

Description

example

[Price,SwapRate,AI,RecCF,RecCFDates,PayCF,PayCFDates] =
swapbyzero(RateSpec,LegRate,Settle,Maturity)
prices a swap instrument. You can use 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 [].

example

[Price,SwapRate,AI,RecCF,RecCFDates,PayCF,PayCFDates] =
swapbyzero(RateSpec,LegRate,Settle,Maturity,Name,Value)
prices a swap instrument with additional options specified by one or more 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

collapse all

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 =

  Columns 1 through 7

   -1.8219    2.5000    2.5000    2.5137    2.4932    2.4932    2.5000

  Columns 8 through 12

    2.5000    2.5000    2.5137    2.4932  102.4932


RecCFDates =

  Columns 1 through 6

      734297      734396      734761      735129      735493      735857

  Columns 7 through 12

      736222      736588      736953      737320      737684      738049


PayCF =

  Columns 1 through 7

   -0.3644    0.5000    1.4048    1.9961    2.8379    3.2760    3.8218

  Columns 8 through 12

    4.1733    4.5164    4.4920    4.7950  104.6608


PayCFDates =

  Columns 1 through 6

      734297      734396      734761      735129      735493      735857

  Columns 7 through 12

      736222      736588      736953      737320      737684      738049

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: [4×2 double]
            Rates: [4×2 double]
         EndTimes: [4×1 double]
       StartTimes: [4×1 double]
         EndDates: [4×1 double]
       StartDates: 734990
    ValuationDate: 734990
            Basis: 0
     EndMonthRule: 1

Look at the Rates for the two interest-rate curves.

RateSpec.Rates
ans =

    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 =

    3.9688    3.6869
    1.9844    1.8434
    3.9688    3.6869

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 =

    3.9693
    1.9846
    3.9693

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: [7×1 double]
            Rates: [7×1 double]
         EndTimes: [7×1 double]
       StartTimes: [7×1 double]
         EndDates: [7×1 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

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)
isbusday(RecCFDates1)

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

  11×11 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


ans =

  11×1 logical array

   1
   1
   1
   1
   1
   0
   1
   1
   1
   1
   0


ans =

  11×11 char array

05-Jan-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


ans =

  11×1 logical array

   1
   1
   1
   1
   1
   1
   1
   1
   1
   1
   1

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';
Period = 1;
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 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

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

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 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 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 = [1 1]; % 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 =

   1.2569e+06

Related Examples

Input Arguments

collapse all

Interest-rate structure, specified using intenvset to create a RateSpec.

RateSpec can also be a 1-by-2 input variable of RateSpecs, 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

Number of instruments, 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

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 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 Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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

collapse all

Reset frequency per year for each swap, specified as NINST-by-2 vector.

Data Types: double

Day-count basis representing the basis for each leg. 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

Notional principal amounts or principal value schedules, specified as 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

Leg type, specified as 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

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 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

Flag to adjust cash flows based on actual period day count, specified as 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

Business day conventions, specified by a character vector or a N-by-1 (or NINST-by-2 if BusDayConvention 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 used in computing business days, specified as MATLAB date numbers using a NHolidays-by-1 vector.

Data Types: double

Rate for the next floating payment, set at the last reset date, specified as a scaler.

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

Rate curve used in generating cash flows for the floating leg of the swap, specified as 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

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Foreign exchange (FX) rate applied to cash flows, specified as an 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

Flag to indicate if initial Principal is exchanged, specified as an NINST-by-1 array of logicals.

Data Types: logical

Flag to indicate if Principal is exchanged at Maturity, specified as an 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

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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.

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.

Accrued interest, returned as a NINST-by-NUMCURVES 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.

Payment dates for the receiving leg, returned as an NINST-by-NUMCURVES matrix.

Cash flows for the paying leg, returned as an NINST-by-NUMCURVES matrix.

Payment dates for the paying leg, returned as an NINST-by-NUMCURVES matrix.

More About

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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

Hull, J. Options, Futures and Other Derivatives Fourth Edition. Prentice Hall, 2000.

Introduced before R2006a

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