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Price swap instrument from set of zero curves and price cross-currency swaps
[Price,SwapRate,AI,RecCF,RecCFDates,PayCF,PayCFDates]
= swapbyzero(RateSpec,LegRate,Settle,Maturity)
[Price,SwapRate,AI,RecCF,RecCFDates,PayCF,PayCFDates]
= swapbyzero(RateSpec,LegRate,Settle,Maturity,Name,Value)
[
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.
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 =
-1.8219 2.5000 2.5000 2.5137 2.4932 2.4932 2.5000 2.5000 2.5000 2.5137 2.4932 102.4932
RecCFDates =
734297 734396 734761 735129 735493 735857 736222 736588 736953 737320 737684 738049
PayCF =
-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 =
734297 734396 734761 735129 735493 735857 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
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 =
3.9693
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
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 = 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'
isbusday(RecCFDates1)
ans = 11×1 logical array
1
1
1
1
1
0
1
1
1
1
0
[Price2,SwapRate2,~,~,RecCFDates2,~,PayCFDates2] = swapbyzero(RateSpec,LegRate,Settle,Maturity,... 'StartDate',StartDate,'BusinessDayConvention','follow'); datestr(RecCFDates2)
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'
isbusday(RecCFDates2)
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
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
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
RateSpec
— Interest-rate structureInterest-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
— Number of instrumentsNumber 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
Settle
— Settlement dateSettlement 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 dateMaturity 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
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
.
[Price,SwapRate,AI,RecCF,RecCFDates,PayCF,PayCFDates]
= swapbyzero(RateSpec,LegRate,Settle,
Maturity,'LegType',LegType,'LatestFloatingRate',LatestFloatingRate,'AdjustCashFlowsBasis',true,
'BusinessDayConvention','modifiedfollow')
'LegReset'
— Reset frequency per year for each swap[1 1]
(default) | vectorReset frequency per year for each swap, specified as NINST
-by-2
vector.
Data Types: double
'Basis'
— Day-count basis of instrument0
(actual/actual) (default) | integer from 0
to 13
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
'Principal'
— Notional principal amounts or principal value schedules100
(default) | vector or cell arrayNotional 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
'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 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 days1
(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 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 countfalse
(default) | value of 0
(false) or 1
(true)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
'BusDayConvention'
— Business day conventionsactual
(default) | character vector | cell array of character vectorsBusiness 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'
— Holidays used in computing business daysholidays.m
(default) | MATLAB^{®} date numbersHolidays used in computing business days, specified as MATLAB date
numbers using a NHolidays
-by-1
vector.
Data Types: double
'LatestFloatingRate'
— Rate for the next floating paymentRateSpec
must contain this information (default) | scalarRate 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
'ProjectionCurve'
— Rate curve used in generating cash flows for the floating leg of the swapProjectionCurve
is not
specified, then RateSpec
is used both for discounting
and generating cash flows for the floating leg (default) | RateSpec
or vectorRate 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
'FXRate'
— Foreign exchange (FX) rate applied to cash flowsswapbyzero
are in same currency (default) | arrayForeign 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
'ExchangeInitialPrincipal'
— Flag to indicate if initial Principal
is exchanged0
(false) (default) | arrayFlag to indicate if initial Principal
is
exchanged, specified as an NINST
-by-1
array
of logicals.
Data Types: logical
'ExchangeMaturityPrincipal'
— Flag to indicate if Principal
exchanged at Maturity
1
(true) (default) | arrayPrice
— Swap pricesSwap 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 legRates 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 interestAccrued interest, returned as a NINST
-by-NUMCURVES
matrix.
RecCF
— Cash flows for receiving legCash flows for the receiving leg, returned as a NINST
-by-NUMCURVES
matrix.
Note:
If there is more than one curve specified in the |
RecCFDates
— Payment dates for receiving legPayment dates for the receiving leg, returned as an NINST
-by-NUMCURVES
matrix.
PayCF
— Cash flows for paying legCash flows for the paying leg, returned as an NINST
-by-NUMCURVES
matrix.
PayCFDates
— Payment dates for paying legPayment dates for the paying leg, returned as an NINST
-by-NUMCURVES
matrix.
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.
Agreement to enter into an interest-rate swap arrangement on a fixed date in future.
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.
Hull, J. Options, Futures and Other Derivatives Fourth Edition. Prentice Hall, 2000.
bondbyzero
| cfbyzero
| fixedbyzero
| floatbyzero
| intenvset
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