simTermStructs

Simulate term structures for LIBOR Market Model

Syntax

[ZeroRates,ForwardRates] = simTermStructs(LMM,nPeriods)

[ZeroRates,ForwardRates] = simTermStructs(___,Name,Value)

Description

[ZeroRates,ForwardRates] = simTermStructs(LMM,nPeriods) simulates future zero curve paths using a specified LiborMarketModel object.

[ZeroRates,ForwardRates] = simTermStructs(___,Name,Value) adds optional name-value pair arguments.

Examples

Simulate Term Structures for a LIBOR Market Model

Create a LMM object.

Settle = datenum('15-Dec-2007');
CurveTimes = [1:5 7 10 20]';
ZeroRates = [.01 .018 .024 .029 .033 .034 .035 .034]';
CurveDates = daysadd(Settle,360*CurveTimes,1);
 
irdc = IRDataCurve('Zero',Settle,CurveDates,ZeroRates);
 
LMMVolFunc = @(a,t) (a(1)*t + a(2)).*exp(-a(3)*t) + a(4);
LMMVolParams = [.3 -.02 .7 .14];
  
numRates = 20;
VolFunc(1:numRates-1) = {@(t) LMMVolFunc(LMMVolParams,t)};
  
Beta = .08;
CorrFunc = @(i,j,Beta) exp(-Beta*abs(i-j));
Correlation = CorrFunc(meshgrid(1:numRates-1)',meshgrid(1:numRates-1),Beta);
  
LMM = LiborMarketModel(irdc,VolFunc,Correlation,'Period',1)

LMM = 
  LiborMarketModel with properties:

       ZeroCurve: [1x1 IRDataCurve]
    VolFunctions: {1x19 cell}
     Correlation: [19x19 double]
      NumFactors: NaN
          Period: 1

Simulate the term structures for the specified LMM object.

[ZeroRates, ForwardRates] = simTermStructs(LMM, 20,'nTrials',100);

Input Arguments

LMM — LiborMarketModel object

object

LiborMarketModel object, specified using the LMM object created using LiborMarketModel.

Data Types: object

nPeriods — Number of simulation periods

numeric

Number of simulation periods, specified as a numeric value. The nPeriods value is determined by the swaption expiry and the periodicity of the rates of the model. For example, if you were to price a swaption expiring in 5 years with a semiannual LIBOR Market Model (LMM), then nPeriods would be 10.

Data Types: 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 quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: [ZeroRates, ForwardRates] = simTermStructs(LMM, 20,'nTrials',100)

'nTrials' — Number of simulated trials

1 (default) | positive integer

Number of simulated trials (sample paths), specified as the comma-separated pair consisting of 'nTrials' and a positive scalar integer value of nPeriods observations each. If you do not specify a value for this argument, the default is 1, indicating a single path of correlated state variables.

Data Types: double

'antithetic' — Flag indicating whether antithetic sampling is used to generate Gaussian random variates

false (default) | positive integer

Flag indicating whether antithetic sampling is used to generate the Gaussian random variates that drive the zero-drift, unit-variance rate Brownian vector dW(t), specified as the comma-separated pair consisting of 'antithetic' and a Boolean scalar flag. For details on the Brownian vector, see simBySolution.

Data Types: logical

'Z' — Direct specification of dependent random noise process

generated by simBySolution function (default) | numeric

Direct specification of the dependent random noise process, specified as the comma-separated pair consisting of 'Z' and a numeric value. The Z value is used to generate the zero-drift, unit-variance rate Brownian vector dW(t) that drives the simulation. For details, see simBySolution for the GBM model.

Data Types: double

'Tenor' — Maturities to compute at each time step

number of rates in LiborMarketModel object (default) | numeric vector

Maturities to compute at each time step, specified as the comma-separated pair consisting of 'Tenor' and a numeric vector.

Tenor enables you to choose a different set of rates to output than the underlying rates. For example, you may want to simulate quarterly data but only report annual rates; this can be done by specifying the optional input Tenor.

The default for tenor is the number of rates in the LiborMarketModel object as specified by the Correlation and VolFunc input arguments for the LiborMarketModel object.

Data Types: double

Output Arguments

ZeroRates — Simulated zero-rate term structures

matrix

Simulated zero-rate term structures, returned as a nPeriods+1-by-nTenors-by-nTrials matrix.

ForwardRates — Simulated forward-rate term structures

matrix

Simulated zero-rate term structures, returned as a nPeriods+1-by-nTenors-by-nTrials matrix.