HullWhite1F class

Create Hull-White one-factor model

Description

The Hull-White one-factor model is specified using the zero curve, alpha, and sigma parameters for the equation

dr=[θ(t)a(t)r]dt+σ(t)dW

where:

dr is the change in the short-term interest rate over a small interval.

r is the short-term interest rate.

Θ(t) is a function of time determining the average direction in which r moves, chosen such that movements in r are consistent with today's zero coupon yield curve.

α is the mean reversion rate.

dt is a small change in time.

σ is the annual standard deviation of the short rate.

W is the Brownian motion.

Construction

OBJ = HullWhite1F(ZeroCurve,alpha,sigma) constructs an object for a Hull-White one-factor model.

For example:

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);
    
alpha = .1;
sigma = .01;
 
HW1F = HullWhite1F(irdc,alpha,sigma);

Properties

The following properties are from the HullWhite1F class.

ZeroCurve

ZeroCurve is specified using the output from IRDataCurve or RateSpec. This is the zero curve used to evolve the path of future interest rates.

Attributes:

SetAccesspublic
GetAccesspublic

Alpha

Mean reversion specified either as a scalar or function handle which takes time as an input and returns a scalar mean reversion value.

Attributes:

SetAccesspublic
GetAccesspublic

Sigma

Volatility specified either as a scalar or function handle which takes time as an input and returns a scalar mean volatility.

Attributes:

SetAccesspublic
GetAccesspublic

Methods

simTermStructsSimulate term structures for Hull-White one-factor model

Definitions

Hull-White One-Factor Model

The Hull-White model is a single-factor, no-arbitrage yield curve model in which the short-term rate of interest is the random factor or state variable. No-arbitrage means that the model parameters are consistent with the bond prices implied in the zero coupon yield curve.

Copy Semantics

Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB® documentation.

Examples

expand all

Construct a Hull-White One-Factor Model

Construct a Hull-White one-factor model.

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);

alpha = .1;
sigma = .01;

HW1F = HullWhite1F(irdc,alpha,sigma)
HW1F = 

  HullWhite1F with properties:

    ZeroCurve: [1x1 IRDataCurve]
        Alpha: @(t,V)inAlpha
        Sigma: @(t,V)inSigma

Use the simTermStructs method with the HullWhite1F model to simulate term structures.

SimPaths = simTermStructs(HW1F, 10,'nTrials',100);

References

Hull, J. Options, Futures, and Other Derivatives, Prentice-Hall, 2011.

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