This class represents a normal inverse gaussian process (NIG). More...
Public Member Functions | |
| NormalInverseGaussianProcess (double x0, double alpha, double beta, double mu, double delta, RandomStream streamBrownian, InverseGaussianProcess igP) | |
Given an InverseGaussianProcess igP, constructs a new NormalInverseGaussianProcess. More... | |
| NormalInverseGaussianProcess (double x0, double alpha, double beta, double mu, double delta, RandomStream streamBrownian, RandomStream streamIG1, RandomStream streamIG2, String igType) | |
Constructs a new NormalInverseGaussianProcess. More... | |
| NormalInverseGaussianProcess (double x0, double alpha, double beta, double mu, double delta, RandomStream streamAll, String igType) | |
Same as above, but all umontreal.ssj.rng.RandomStream ’s are set to the same stream, streamAll. | |
| double [] | generatePath () |
| Generates the path. More... | |
| double | nextObservation () |
| Returns the value of the process for the next time step. More... | |
| void | setObservationTimes (double t[], int d) |
| Sets the observation times on the NIG process as usual, but also sets the observation times of the underlying InverseGaussianProcess. More... | |
| void | setParams (double x0, double alpha, double beta, double mu, double delta) |
| Sets the parameters. More... | |
| double | getAlpha () |
| Returns alpha. | |
| double | getBeta () |
| Returns beta. | |
| double | getMu () |
| Returns mu. | |
| double | getDelta () |
| Returns delta. | |
| double | getGamma () |
| Returns gamma. | |
| double | getAnalyticAverage (double time) |
| Returns the analytic average, which is \(\mu t + \delta t \beta/ \gamma\). | |
| double | getAnalyticVariance (double time) |
| Returns the analytic variance, which is \(\delta t \alpha^2 / \gamma^3\). | |
| RandomStream | getStream () |
| Only returns the stream if all streams are equal, including the stream(s) in the underlying InverseGaussianProcess. | |
| void | setStream (RandomStream stream) |
Sets all internal streams to stream, including the stream(s) of the underlying InverseGaussianProcess. | |
 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... | |
Protected Member Functions | |
| double [] | generatePathTwoIGStreams () |
| void | init () |
| Protected Member Functions inherited from StochasticProcess | |
| void | init () |
Protected Attributes | |
| RandomStream | streamIG1 |
| RandomStream | streamIG2 |
| RandomStream | streamBrownian |
| InverseGaussianProcess | igProcess |
| NormalGen | normalGen |
| double [] | stochTime |
| double | mu |
| double | delta |
| double | alpha |
| double | beta |
| double | gamma |
| 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 |
Package Attributes | |
| double [] | dt |
| double [] | mudt |
Detailed Description
This class represents a normal inverse gaussian process (NIG).
It obeys the stochastic differential equation [15]
\[ dX(t) = \mu dt + dB(h(t)), \tag{nig} \]
where \(\{B(t), t\ge0\}\) is a BrownianMotion with drift \(\beta\) and variance 1, and \(h(t)\) is an InverseGaussianProcess \(IG(\nu/\gamma,\nu^2)\), with \(\nu= \delta dt\) and \(\gamma= \sqrt{\alpha^2 - \beta^2}\).
In this class, the process is generated using the sequential technique: \(X(0)=x_0\) and
\[ X(t_j) - X(t_{j-1}) =\mu dt + \beta Y_j + \sqrt{Y_j} Z_j, \]
where \(Z_j \sim N(0,1)\), and \(Y_j \sim IG(\nu/\gamma,\nu^2)\) with \(\nu= \delta(t_j - t_{j-1})\).
There is one umontreal.ssj.rng.RandomStream used to generate the \(Z_j\)’s and there are one or two streams used to generate the underlying InverseGaussianProcess, depending on which IG subclass is used.
In finance, a NIG process usually means that the log-return is given by a NIG process; GeometricNormalInverseGaussianProcess should be used in that case.
Constructor & Destructor Documentation
◆ NormalInverseGaussianProcess() [1/2]
| NormalInverseGaussianProcess | ( | double | x0, |
| double | alpha, | ||
| double | beta, | ||
| double | mu, | ||
| double | delta, | ||
| RandomStream | streamBrownian, | ||
| InverseGaussianProcess | igP | ||
| ) |
Given an InverseGaussianProcess igP, constructs a new NormalInverseGaussianProcess.
The parameters and observation times of the IG process will be overriden by the parameters of the NIG process. If there are two umontreal.ssj.rng.RandomStream ’s in the InverseGaussianProcess, this constructor assumes that both streams have been set to the same stream.
◆ NormalInverseGaussianProcess() [2/2]
| NormalInverseGaussianProcess | ( | double | x0, |
| double | alpha, | ||
| double | beta, | ||
| double | mu, | ||
| double | delta, | ||
| RandomStream | streamBrownian, | ||
| RandomStream | streamIG1, | ||
| RandomStream | streamIG2, | ||
| String | igType | ||
| ) |
Constructs a new NormalInverseGaussianProcess.
The string argument corresponds to the type of underlying InverseGaussianProcess. The choices are SEQUENTIAL_SLOW, SEQUENTIAL_MSH, BRIDGE and PCA, which correspond respectively to InverseGaussianProcess, InverseGaussianProcessMSH, InverseGaussianProcessBridge and InverseGaussianProcessPCA. The third umontreal.ssj.rng.RandomStream, streamIG2, will not be used at all if the SEQUENTIAL_SLOW or PCA methods are chosen.
Member Function Documentation
◆ generatePath()
| double [] generatePath | ( | ) |
Generates the path.
This method samples each stream alternatively, which is useful for quasi-Monte Carlo, where all streams are in fact the same iterator on a umontreal.ssj.hups.PointSet.
◆ nextObservation()
| double nextObservation | ( | ) |
Returns the value of the process for the next time step.
If the underlying InverseGaussianProcess is of type InverseGaussianProcessPCA, this method cannot be used. It will work with InverseGaussianProcessBridge, but the return order of the observations is the bridge order.
◆ setObservationTimes()
| void setObservationTimes | ( | double | t[], |
| int | d | ||
| ) |
Sets the observation times on the NIG process as usual, but also sets the observation times of the underlying InverseGaussianProcess.
It furthermore sets the starting value of the InverseGaussianProcess to t[0].
◆ setParams()
| void setParams | ( | double | x0, |
| double | alpha, | ||
| double | beta, | ||
| double | mu, | ||
| double | delta | ||
| ) |
Sets the parameters.
Also, computes \(\gamma= \sqrt{\alpha^2-\beta^2}\).
The documentation for this class was generated from the following file:
- NormalInverseGaussianProcess.java
