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 =
4.7594Price 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
Output Arguments
More About
References
[1] Hull, J. Options, Futures and Other Derivatives Fourth Edition. Prentice Hall, 2000.
See Also
bondbyzero | cfbyzero | fixedbyzero | floatbyzero | intenvset
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