Package org.drip.dynamics.sabr

Class StochasticVolatilityStateEvolver

java.lang.Object

org.drip.dynamics.sabr.StochasticVolatilityStateEvolver

All Implemented Interfaces:

PointStateEvolver

public class StochasticVolatilityStateEvolver
extends java.lang.Object
implements PointStateEvolver

StochasticVolatilityStateEvolver provides the SABR Stochastic Volatility Evolution Dynamics.

• Module = Product Core Module
• Library = Fixed Income Analytics
• Project = HJM, Hull White, LMM, and SABR Dynamic Evolution Models
• Package = SABR Based Latent State Evolution

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
StochasticVolatilityStateEvolver(ForwardLabel lslForward, double dblBeta, double dblRho, double dblVolatilityOfVolatility, UnivariateSequenceGenerator usgForwardRate, UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic)	StochasticVolatilityStateEvolver Constructor

Method Summary

Modifier and Type	Method	Description
double	beta()	Retrieve SABR Beta
static StochasticVolatilityStateEvolver	CEV(ForwardLabel lslForward, double dblBeta, double dblRho, UnivariateSequenceGenerator usgForwardRate, UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic)	Create a Constant Elasticity of Variance SABR Instance
ImpliedBlackVolatility	computeATMBlackVolatility(double dblATMForwardRate, double dblTTE, double dblSigma0)	Compute the Implied ATM Black Volatility for the ATM Forward Rate and the TTE
ImpliedBlackVolatility	computeBlackVolatility(double dblStrike, double dblATMForwardRate, double dblTTE, double dblSigma0)	Compute the Implied Black Volatility for the Specified Strike, the ATM Forward Rate, and the TTE
LSQMPointUpdate	evolve(int iSpotDate, int iViewDate, int iSpotTimeIncrement, LSQMPointUpdate lsqmPrev)	Evolve the Latent State and return the LSQM Point Update
ForwardLabel	forwardLabel()	Retrieve the Forward Label
static StochasticVolatilityStateEvolver	Gaussian(ForwardLabel lslForward, double dblRho, double dblVolatilityOfVolatility, UnivariateSequenceGenerator usgForwardRate, UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic)	Create a Gaussian SABR Instance
static StochasticVolatilityStateEvolver	Lognormal(ForwardLabel lslForward, double dblRho, double dblVolatilityOfVolatility, UnivariateSequenceGenerator usgForwardRate, UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic)	Create a Log-normal SABR Instance
double	rho()	Retrieve SABR Rho
UnivariateSequenceGenerator	usgForwardRate()	The Forward Rate Univariate Random Variable Generator Sequence
UnivariateSequenceGenerator	usgForwardRateVolatilityIdiosyncratic()	The Idiosyncratic Component of Forward Rate Volatility Univariate Random Variable Generator Sequence
double	volatilityOfVolatility()	Retrieve SABR Volatility of Volatility

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

StochasticVolatilityStateEvolver

public StochasticVolatilityStateEvolver(ForwardLabel lslForward,
double dblBeta,
double dblRho,
double dblVolatilityOfVolatility,
UnivariateSequenceGenerator usgForwardRate,
UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic)
                                 throws java.lang.Exception

StochasticVolatilityStateEvolver Constructor

Parameters:

lslForward - The Forward Rate Latent State Label

dblBeta - SABR Beta

dblRho - SABR Rho

dblVolatilityOfVolatility - SABR Volatility Of Volatility

usgForwardRate - The Forward Rate Univariate Sequence Generator

usgForwardRateVolatilityIdiosyncratic - The Idiosyncratic Component Forward Rate Volatility Univariate Sequence Generator

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

Gaussian

public static final StochasticVolatilityStateEvolver Gaussian(ForwardLabel lslForward,
double dblRho,
double dblVolatilityOfVolatility,
UnivariateSequenceGenerator usgForwardRate,
UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic)

Create a Gaussian SABR Instance

Parameters:

lslForward - The Forward Rate Latent State Label

dblRho - SABR Rho

dblVolatilityOfVolatility - SABR Volatility Of Volatility

usgForwardRate - The Forward Rate Univariate Sequence Generator

usgForwardRateVolatilityIdiosyncratic - The Idiosyncratic Component Forward Rate Volatility Univariate Sequence Generator

Returns:

The Gaussian SABR Instance

Lognormal

public static final StochasticVolatilityStateEvolver Lognormal(ForwardLabel lslForward,
double dblRho,
double dblVolatilityOfVolatility,
UnivariateSequenceGenerator usgForwardRate,
UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic)

Create a Log-normal SABR Instance

Parameters:

lslForward - The Forward Rate Latent State Label

dblRho - SABR Rho

dblVolatilityOfVolatility - SABR Volatility Of Volatility

usgForwardRate - The Forward Rate Univariate Sequence Generator

usgForwardRateVolatilityIdiosyncratic - The Idiosyncratic Component Forward Rate Volatility Univariate Sequence Generator

Returns:

The Log-normal SABR Instance

CEV

public static final StochasticVolatilityStateEvolver CEV(ForwardLabel lslForward,
double dblBeta,
double dblRho,
UnivariateSequenceGenerator usgForwardRate,
UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic)

Create a Constant Elasticity of Variance SABR Instance

Parameters:

lslForward - The Forward Rate Latent State Label

dblBeta - SABR Beta

dblRho - SABR Rho

usgForwardRate - The Forward Rate Univariate Sequence Generator

usgForwardRateVolatilityIdiosyncratic - The Idiosyncratic Component Forward Rate Volatility Univariate Sequence Generator

Returns:

The Constant Elasticity of Variance SABR Instance

forwardLabel

public ForwardLabel forwardLabel()

Retrieve the Forward Label

Returns:

The Forward Label

volatilityOfVolatility

public double volatilityOfVolatility()

Retrieve SABR Volatility of Volatility

Returns:

SABR Volatility of Volatility

beta

public double beta()

Retrieve SABR Beta

Returns:

SABR Beta

rho

public double rho()

Retrieve SABR Rho

Returns:

SABR Rho

usgForwardRate

public UnivariateSequenceGenerator usgForwardRate()

The Forward Rate Univariate Random Variable Generator Sequence

Returns:

The Forward Rate Univariate Random Variable Generator Sequence

usgForwardRateVolatilityIdiosyncratic

public UnivariateSequenceGenerator usgForwardRateVolatilityIdiosyncratic()

The Idiosyncratic Component of Forward Rate Volatility Univariate Random Variable Generator Sequence

Returns:

The Idiosyncratic Component of Forward Rate Volatility Univariate Random Variable Generator Sequence

evolve

public LSQMPointUpdate evolve(int iSpotDate,
int iViewDate,
int iSpotTimeIncrement,
LSQMPointUpdate lsqmPrev)

Description copied from interface: PointStateEvolver

Evolve the Latent State and return the LSQM Point Update

Specified by:

evolve in interface PointStateEvolver

Parameters:

iSpotDate - The Spot Date

iViewDate - The View Date

iSpotTimeIncrement - The Spot Time Increment

lsqmPrev - The Previous LSQM Point Update

Returns:

The LSQM Point Update

computeATMBlackVolatility

public ImpliedBlackVolatility computeATMBlackVolatility(double dblATMForwardRate,
double dblTTE,
double dblSigma0)

Compute the Implied ATM Black Volatility for the ATM Forward Rate and the TTE

Parameters:

dblATMForwardRate - ATM Forward Rate

dblTTE - Time to Expiry

dblSigma0 - Initial Sigma

Returns:

The Implied Black Volatility Instance

computeBlackVolatility

public ImpliedBlackVolatility computeBlackVolatility(double dblStrike,
double dblATMForwardRate,
double dblTTE,
double dblSigma0)

Compute the Implied Black Volatility for the Specified Strike, the ATM Forward Rate, and the TTE

Parameters:

dblStrike - Strike

dblATMForwardRate - ATM Forward Rate

dblTTE - Time to Expiry

dblSigma0 - Initial Sigma

Returns:

The Implied Black Volatility Instance