The geometric normal inverse gaussian (GNIG) process is the exponentiation of a NormalInverseGaussianProcess : More...
Public Member Functions | |
| GeometricNormalInverseGaussianProcess (double s0, double muGeom, double alpha, double beta, double mu, double delta, RandomStream streamBrownian, NormalInverseGaussianProcess nigP) | |
| Constructs a new GeometricNormalInverseGaussianProcess. | |
| GeometricNormalInverseGaussianProcess (double s0, double muGeom, double alpha, double beta, double mu, double delta, RandomStream streamBrownian, InverseGaussianProcess igP) | |
| Constructs a new GeometricNormalInverseGaussianProcess. | |
| GeometricNormalInverseGaussianProcess (double s0, double muGeom, double alpha, double beta, double mu, double delta, RandomStream streamBrownian, RandomStream streamNIG1, RandomStream streamNIG2, String igType) | |
| Constructs a new GeometricNormalInverseGaussianProcess. | |
| GeometricNormalInverseGaussianProcess (double s0, double muGeom, double alpha, double beta, double mu, double delta, RandomStream streamAll, String igType) | |
| Constructs a new GeometricNormalInverseGaussianProcess. | |
| Public Member Functions inherited from umontreal.ssj.stochprocess.GeometricLevyProcess | |
| double[] | generatePath () |
| Generates a path. | |
| double | nextObservation () |
| Returns the next observation. | |
| void | resetStartProcess () |
| Resets the step counter of the geometric process and the underlying Lévy process to the start value. | |
| void | setObservationTimes (double[] time, int d) |
| Sets the observation times on the geometric process and the underlying Lévy process. | |
| double | getOmega () |
| Returns the risk neutral correction. | |
| double | getMuGeom () |
| Returns the geometric drift parameter, which is usually the interest rate, \(r\). | |
| void | setMuGeom (double muGeom) |
| Sets the drift parameter (interest rate) of the geometric term. | |
| StochasticProcess | getLevyProcess () |
| Returns the Lévy process. | |
| void | resetRiskNeutralCorrection (double omegaRN) |
| Changes the value of \(\omega_{RN}\). | |
| RandomStream | getStream () |
| Returns the stream from the underlying Lévy process. | |
| void | setStream (RandomStream stream) |
| Resets the stream in the underlying Lévy process. | |
| Public Member Functions inherited from umontreal.ssj.stochprocess.StochasticProcess | |
| void | setObservationTimes (double delta, int d) |
| Sets equidistant observation times at \(t_j = j\delta\), for. | |
| double[] | getObservationTimes () |
| Returns a reference to the array that contains the observation times. | |
| int | getNumObservationTimes () |
| Returns the number \(d\) of observation times, excluding the time \(t_0\). | |
| double[] | generatePath (RandomStream stream) |
| Same as generatePath(), but first resets the stream to stream. | |
| double[] | getPath () |
| Returns a reference to the last generated sample path \(\{X(t_0), ... ,
X(t_d)\}\). | |
| void | getSubpath (double[] subpath, int[] pathIndices) |
| Returns in subpath the values of the process at a subset of the observation times, specified as the times \(t_j\) whose indices. | |
| double | getObservation (int j) |
| Returns \(X(t_j)\) from the current sample path. | |
| boolean | hasNextObservation () |
| Returns true if \(j<d\), where \(j\) is the number of observations of the current sample path generated since the last call to resetStartProcess. | |
| int | getCurrentObservationIndex () |
| Returns the value of the index \(j\) corresponding to the time. | |
| double | getCurrentObservation () |
| Returns the value of the last generated observation \(X(t_j)\). | |
| double | getX0 () |
| Returns the initial value \(X(t_0)\) for this process. | |
| void | setX0 (double s0) |
| Sets the initial value \(X(t_0)\) for this process to s0, and reinitializes. | |
| int[] | getArrayMappingCounterToIndex () |
| Returns a reference to an array that maps an integer \(k\) to \(i_k\), the index of the observation \(S(t_{i_k})\) corresponding to the. | |
Detailed Description
The geometric normal inverse gaussian (GNIG) process is the exponentiation of a NormalInverseGaussianProcess :
\[ S(t) = S_0 \exp\left[ (r-\omega_{RN})t + \mbox{NIG}(t;\alpha,\beta,\mu,\delta) \right], \]
where \(r\) is the interest rate. It is a strictly positive process, which is useful in finance. There is also a neutral correction in the exponential, \(\omega_{RN}= \mu+ \delta\gamma-\delta\sqrt{\alpha^2-(1+\beta)^2}\), which takes into account the market price of risk. The underlying NIG process must start at zero, NIG \((t_0) = 0 \) and the initial time should also be set to zero,
\(t_0 = 0\), both for the NIG and GNIG.
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Definition at line 46 of file GeometricNormalInverseGaussianProcess.java.
Constructor & Destructor Documentation
◆ GeometricNormalInverseGaussianProcess() [1/4]
| umontreal.ssj.stochprocess.GeometricNormalInverseGaussianProcess.GeometricNormalInverseGaussianProcess | ( | double | s0, |
| double | muGeom, | ||
| double | alpha, | ||
| double | beta, | ||
| double | mu, | ||
| double | delta, | ||
| RandomStream | streamBrownian, | ||
| NormalInverseGaussianProcess | nigP ) |
Constructs a new GeometricNormalInverseGaussianProcess.
The parameters of the NIG process will be overwritten by the parameters given to the GNIG, with the initial value of the NIG set to 0. The observation times of the NIG will also be changed to those of the GNIG.
Definition at line 54 of file GeometricNormalInverseGaussianProcess.java.
◆ GeometricNormalInverseGaussianProcess() [2/4]
| umontreal.ssj.stochprocess.GeometricNormalInverseGaussianProcess.GeometricNormalInverseGaussianProcess | ( | double | s0, |
| double | muGeom, | ||
| double | alpha, | ||
| double | beta, | ||
| double | mu, | ||
| double | delta, | ||
| RandomStream | streamBrownian, | ||
| InverseGaussianProcess | igP ) |
Constructs a new GeometricNormalInverseGaussianProcess.
The process igP will be used internally by the underlying
Definition at line 70 of file GeometricNormalInverseGaussianProcess.java.
◆ GeometricNormalInverseGaussianProcess() [3/4]
| umontreal.ssj.stochprocess.GeometricNormalInverseGaussianProcess.GeometricNormalInverseGaussianProcess | ( | double | s0, |
| double | muGeom, | ||
| double | alpha, | ||
| double | beta, | ||
| double | mu, | ||
| double | delta, | ||
| RandomStream | streamBrownian, | ||
| RandomStream | streamNIG1, | ||
| RandomStream | streamNIG2, | ||
| String | igType ) |
Constructs a new GeometricNormalInverseGaussianProcess.
The drift of the geometric term, muGeom, is usually the interest rate
\(r\). s0 is the initial value of the process and the other four parameters are the parameters of the underlying NormalInverseGaussianProcess process.
Definition at line 88 of file GeometricNormalInverseGaussianProcess.java.
◆ GeometricNormalInverseGaussianProcess() [4/4]
| umontreal.ssj.stochprocess.GeometricNormalInverseGaussianProcess.GeometricNormalInverseGaussianProcess | ( | double | s0, |
| double | muGeom, | ||
| double | alpha, | ||
| double | beta, | ||
| double | mu, | ||
| double | delta, | ||
| RandomStream | streamAll, | ||
| String | igType ) |
Constructs a new GeometricNormalInverseGaussianProcess.
The String igType corresponds to the type of InverseGaussianProcess that will be used by the underlying
NormalInverseGaussianProcess. All umontreal.ssj.rng.RandomStream ’s used to generate the underlying NormalInverseGaussianProcess and its underlying InverseGaussianProcess are set to the same given streamAll.
Definition at line 108 of file GeometricNormalInverseGaussianProcess.java.
The documentation for this class was generated from the following file:
- src/main/java/umontreal/ssj/stochprocess/GeometricNormalInverseGaussianProcess.java
