Module net.finmath.lib

Package net.finmath.fouriermethod.models

Class MertonModel

java.lang.Object

net.finmath.fouriermethod.models.MertonModel

All Implemented Interfaces:

CharacteristicFunctionModel, Model

public class MertonModel
extends Object
implements CharacteristicFunctionModel

Implements the characteristic function of a Merton jump diffusion model. The model is \[ dS = \mu S dt + \sigma S dW + S dJ, \quad S(0) = S_{0}, \] \[ dN = r N dt, \quad N(0) = N_{0}, \] where \( W \) is Brownian motion and \( J \) is a jump process (compound Poisson process). The process \( J \) is given by \( J(t) = \sum_{i=1}^{N(t)} (Y_{i}-1) \), where \( \log(Y_{i}) \) are i.i.d. normals with mean \( a - \frac{1}{2} b^{2} \) and standard deviation \( b \). Here \( a \) is the jump size mean and \( b \) is the jump size std. dev.

Version:

1.0

Author:

Alessandro Gnoatto

Constructor Summary

Constructors

Constructor	Description
MertonModel(double initialValue, double riskFreeRate, double volatility, double jumpIntensity, double jumpSizeMean, double jumpSizeStdDev)	Construct a single curve Merton jump diffusion model.
MertonModel(double initialValue, double riskFreeRate, double discountRate, double volatility, double jumpIntensity, double jumpSizeMean, double jumpSizeStdDev)	Construct a Merton jump diffusion model with constant rates for the forward price (i.e.
MertonModel(LocalDate referenceDate, double initialValue, DiscountCurve discountCurveForForwardRate, DiscountCurve discountCurveForDiscountRate, double volatility, double jumpIntensity, double jumpSizeMean, double jumpSizeStdDev)	Construct a Merton jump diffusion model with discount curves for the forward price (i.e.

Method Summary

Modifier and Type	Method	Description
CharacteristicFunction	apply(double time)	Returns the characteristic function of X(t), where X is this stochastic process.
DiscountCurve	getDiscountCurveForDiscountRate()
DiscountCurve	getDiscountCurveForForwardRate()
double	getDiscountRate()
double	getInitialValue()
double	getJumpIntensity()
double	getJumpSizeMean()
double	getJumpSizeStdDev()
LocalDate	getReferenceDate()
double	getRiskFreeRate()
double	getVolatility()
String	toString()

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

MertonModel

public MertonModel(LocalDate referenceDate,
                   double initialValue,
                   DiscountCurve discountCurveForForwardRate,
                   DiscountCurve discountCurveForDiscountRate,
                   double volatility,
                   double jumpIntensity,
                   double jumpSizeMean,
                   double jumpSizeStdDev)

Construct a Merton jump diffusion model with discount curves for the forward price (i.e. repo rate minus dividend yield) and for discounting.

Parameters:

referenceDate - The date representing the time t = 0. All other double times are following FloatingpointDate.

initialValue - \( S_{0} \) - spot - initial value of S

discountCurveForForwardRate - The curve specifying \( t \mapsto exp(- r^{\text{c}}(t) \cdot t) \) - with \( r^{\text{c}}(t) \) the risk free rate

volatility - \( \sigma \) the initial volatility level

jumpIntensity - Coefficients of for the jump intensity.

jumpSizeMean - Jump size mean

jumpSizeStdDev - Jump size variance.

discountCurveForDiscountRate - The curve specifying \( t \mapsto exp(- r^{\text{d}}(t) \cdot t) \) - with \( r^{\text{d}}(t) \) the discount rate

MertonModel

public MertonModel(double initialValue,
                   double riskFreeRate,
                   double discountRate,
                   double volatility,
                   double jumpIntensity,
                   double jumpSizeMean,
                   double jumpSizeStdDev)

Construct a Merton jump diffusion model with constant rates for the forward price (i.e. repo rate minus dividend yield) and for the discount curve.

Parameters:

initialValue - \( S_{0} \) - spot - initial value of S

riskFreeRate - The constant risk free rate for the drift (repo rate of the underlying).

volatility - \( \sigma \) the initial volatility level

jumpIntensity - Coefficients of for the jump intensity.

jumpSizeMean - Jump size mean

jumpSizeStdDev - Jump size variance.

discountRate - The constant rate used for discounting.

MertonModel

public MertonModel(double initialValue,
                   double riskFreeRate,
                   double volatility,
                   double jumpIntensity,
                   double jumpSizeMean,
                   double jumpSizeStdDev)

Construct a single curve Merton jump diffusion model.

Parameters:

initialValue - \( S_{0} \) - spot - initial value of S

riskFreeRate - The constant risk free rate for the drift (repo rate of the underlying). It is also used for discounting.

volatility - \( \sigma \) the initial volatility level

jumpIntensity - Coefficients of for the jump intensity.

jumpSizeMean - Jump size mean

jumpSizeStdDev - Jump size variance.

Method Detail

apply

public CharacteristicFunction apply(double time)

Description copied from interface: CharacteristicFunctionModel

Returns the characteristic function of X(t), where X is this stochastic process.

Specified by:

apply in interface CharacteristicFunctionModel

Parameters:

time - The time at which the stochastic process is observed.

Returns:

The characteristic function of X(t).

getReferenceDate

public LocalDate getReferenceDate()

Returns:

the referenceDate

getInitialValue

public double getInitialValue()

Returns:

the initialValue

getDiscountCurveForForwardRate

public DiscountCurve getDiscountCurveForForwardRate()

Returns:

the discountCurveForForwardRate

getRiskFreeRate

public double getRiskFreeRate()

Returns:

the riskFreeRate

getDiscountCurveForDiscountRate

public DiscountCurve getDiscountCurveForDiscountRate()

Returns:

the discountCurveForDiscountRate

getDiscountRate

public double getDiscountRate()

Returns:

the discountRate

getVolatility

public double getVolatility()

Returns:

the volatility

getJumpIntensity

public double getJumpIntensity()

Returns:

the jumpIntensity

getJumpSizeMean

public double getJumpSizeMean()

Returns:

the jumpSizeMean

getJumpSizeStdDev

public double getJumpSizeStdDev()

Returns:

the jumpSizeStdDev

toString

public String toString()

Overrides:

toString in class Object