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simTermStructs

Simulate term structures for two-factor additive Gaussian interest-rate model

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Syntax

[ZeroRates,ForwardRates] = simTermStructs(G2PP,nPeriods)
[ZeroRates,ForwardRates] = simTermStructs(___,Name,Value)

Description

[ZeroRates,ForwardRates] = simTermStructs(G2PP,nPeriods) simulates future zero curve paths using a specified LinearGaussian2F object.

example

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

example

Examples

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Open Live Script

Create a two-factor additive Gaussian interest-rate model. 

Settle = datetime(2007,12,15);
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);
    
a = .07;
b = .5;
sigma = .01;
eta = .006;
rho = -.7;
 
G2PP = LinearGaussian2F(irdc,a,b,sigma,eta,rho)
G2PP = 
  LinearGaussian2F with properties:

    ZeroCurve: [1x1 IRDataCurve]
            a: @(t,V)ina
            b: @(t,V)inb
        sigma: @(t,V)insigma
          eta: @(t,V)ineta
          rho: -0.7000

Use the simTermStructs method to simulate term structures based on the LinearGaussian2F model. 

 SimPaths = simTermStructs(G2PP, 10,'nTrials',100);
Open Live Script

Create a two-factor additive Gaussian interest-rate model. 

Settle = datetime(2007,12,15);
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);
a = .07;
b = .5;
sigma = .01;
eta = .006;
rho = -.7;
G2PP = LinearGaussian2F(irdc,a,b,sigma,eta,rho)
G2PP = 
  LinearGaussian2F with properties:

    ZeroCurve: [1x1 IRDataCurve]
            a: @(t,V)ina
            b: @(t,V)inb
        sigma: @(t,V)insigma
          eta: @(t,V)ineta
          rho: -0.7000

Use the simTermStructs method to simulate term structures based on the LinearGaussian2F object, where uneven simulation tenors are specified using the optional name-value argument deltaTime as a vector of length NPeriods. 

NPeriods = 10;               
dt = rand(NPeriods,1);
SimPaths = G2PP.simTermStructs(NPeriods,'nTrials',100,'DeltaTime',dt);

Input Arguments

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LinearGaussian2F object, specified using the G2PP object created using LinearGaussian2F.

Data Types: object

Number of simulation periods, specified as a numeric value. For example, to simulate 12 years with an annual spacing, specify 12 as the nPeriods input and 1 as the optional deltaTime input (note that the default value for deltaTime is 1).

Data Types: 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: [ZeroRates,ForwardRates] = simTermStructs(G2PP,NPeriods,'nTrials',100,'deltaTime',dt)

Time step between nPeriods, specified as the comma-separated pair consisting of 'deltaTime' and a numeric scalar or vector. For example, to simulate 12 years with an annual spacing, specify 12 as the nPeriods input and 1 as the optional deltaTime input (note that the default value for deltaTime is 1).

Data Types: double

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

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, see simBySolution for the HWV model.

Data Types: logical

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 HWV model. If you do not specify a value for Z, simBySolution generates Gaussian variates.

Data Types: double

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.

Data Types: double

Output Arguments

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

Simulated zero-rate term structures, returned as a nPeriods+1-by-nTenors-by-nTrials matrix. The ForwardRates output is computed using the simulated short rates and by using the model definition to recover the entire yield curve at each simulation date.

Version History

Introduced in R2013a

See Also

Topics