MertonModel (finmath lib 4.0.13 API)

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 and 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. repo rate minus dividend yield) and for the discount curve.
`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.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and 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

Class MertonModel

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

MertonModel

MertonModel

MertonModel

Method Detail

apply

getReferenceDate

getInitialValue

getDiscountCurveForForwardRate

getRiskFreeRate

getDiscountCurveForDiscountRate

getDiscountRate

getVolatility

getJumpIntensity

getJumpSizeMean

getJumpSizeStdDev

toString