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. 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. More... | |
| GeometricNormalInverseGaussianProcess (double s0, double muGeom, double alpha, double beta, double mu, double delta, RandomStream streamBrownian, InverseGaussianProcess igP) | |
Constructs a new GeometricNormalInverseGaussianProcess. More... | |
| 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. More... | |
| GeometricNormalInverseGaussianProcess (double s0, double muGeom, double alpha, double beta, double mu, double delta, RandomStream streamAll, String igType) | |
Constructs a new GeometricNormalInverseGaussianProcess. More... | |
 Public Member Functions inherited from GeometricLevyProcess | |
| double [] | generatePath () |
| Generates a path. | |
| double | nextObservation () |
| Returns the next observation. More... | |
| 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 \(\omega_{RN}\). More... | |
| RandomStream | getStream () |
| Returns the stream from the underlying Lévy process. More... | |
| void | setStream (RandomStream stream) |
| Resets the stream in the underlying Lévy process. More... | |
| Public Member Functions inherited from StochasticProcess | |
| void | setObservationTimes (double[] T, int d) |
Sets the observation times of the process to a copy of T, with. More... | |
| void | setObservationTimes (double delta, int d) |
| Sets equidistant observation times at \(t_j = j\delta\), for. More... | |
| double [] | getObservationTimes () |
| Returns a reference to the array that contains the observation times. More... | |
| int | getNumObservationTimes () |
| Returns the number \(d\) of observation times, excluding the time \(t_0\). | |
| abstract double [] | generatePath () |
| Generates, returns, and saves the sample path \(\{X(t_0), X(t_1), \dots, X(t_d)\}\). More... | |
| 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 \(\{X(t_0), ... , X(t_d)\}\). More... | |
| 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. More... | |
| double | getObservation (int j) |
| Returns \(X(t_j)\) from the current sample path. More... | |
| void | resetStartProcess () |
| Resets the observation counter to its initial value \(j=0\), so that the current observation \(X(t_j)\) becomes \(X(t_0)\). More... | |
| 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. More... | |
| double | nextObservation () |
| Generates and returns the next observation \(X(t_j)\) of the stochastic process. More... | |
| int | getCurrentObservationIndex () |
| Returns the value of the index \(j\) corresponding to the time. More... | |
| 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. | |
| abstract void | setStream (RandomStream stream) |
Resets the random stream of the underlying generator to stream. | |
| abstract RandomStream | getStream () |
| Returns the random stream of the underlying generator. | |
| 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 \(k\)-th observation to be generated for a sample path of this process. More... | |
Additional Inherited Members | |
| Protected Member Functions inherited from GeometricLevyProcess | |
| void | init () |
| Protected Member Functions inherited from StochasticProcess | |
| void | init () |
| Protected Attributes inherited from GeometricLevyProcess | |
| StochasticProcess | levyProcess |
| double | omegaRiskNeutralCorrection |
| double | muGeom |
| double [] | muGeomRNdt |
| double [] | muGeomRNdT |
| Protected Attributes inherited from StochasticProcess | |
| boolean | observationTimesSet = false |
| double | x0 = 0.0 |
| int | d = -1 |
| int | observationIndex = 0 |
| int | observationCounter = 0 |
| double [] | t |
| double [] | path |
| int [] | observationIndexFromCounter |
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.
Constructor & Destructor Documentation
◆ GeometricNormalInverseGaussianProcess() [1/4]
| 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.
◆ GeometricNormalInverseGaussianProcess() [2/4]
| 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 NormalInverseGaussianProcess.
◆ GeometricNormalInverseGaussianProcess() [3/4]
| 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.
◆ GeometricNormalInverseGaussianProcess() [4/4]
| 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.
The documentation for this class was generated from the following file:
- GeometricNormalInverseGaussianProcess.java
