Represents a geometric Brownian motion (GBM) process \(\{S(t), t\ge0\}\), which evolves according to the stochastic differential equation. More...
Public Member Functions | |
| GeometricBrownianMotion (double s0, double mu, double sigma, RandomStream stream) | |
Same as GeometricBrownianMotion (s0, mu, sigma, new BrownianMotion (0.0, 0.0, 1.0, stream)). | |
| GeometricBrownianMotion (double s0, double mu, double sigma, BrownianMotion bm) | |
Constructs a new GeometricBrownianMotion with parameters \(\mu= \mathtt{mu}\), \(\sigma= \mathtt{sigma}\), and \(S(t_0) = \mathtt{s0}\), using bm as the underlying BrownianMotion. More... | |
| void | setObservationTimes (double[] t, int d) |
| double | nextObservation () |
| double [] | generatePath () |
| double [] | generatePath (RandomStream stream) |
| void | resetStartProcess () |
Same as in StochasticProcess, but also invokes resetStartProcess for the underlying BrownianMotion object. | |
| void | setParams (double s0, double mu, double sigma) |
| Sets the parameters \(S(t_0) = \mathtt{s0}\), \(\mu= \mathtt{mu}\) and \(\sigma= \mathtt{sigma}\) of the process. More... | |
| void | setStream (RandomStream stream) |
Resets the umontreal.ssj.rng.RandomStream for the underlying Brownian motion to stream. | |
| RandomStream | getStream () |
| Returns the umontreal.ssj.rng.RandomStream for the underlying Brownian motion. | |
| double | getMu () |
| Returns the value of \(\mu\). | |
| double | getSigma () |
| Returns the value of \(\sigma\). | |
| NormalGen | getGen () |
| Returns the umontreal.ssj.randvar.NormalGen used. | |
| BrownianMotion | getBrownianMotion () |
| Returns a reference to the BrownianMotion object used to generate the process. | |
 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 | |
| void | init () |
| Protected Member Functions inherited from StochasticProcess | |
| void | init () |
Protected Attributes | |
| NormalGen | gen |
| BrownianMotion | bm |
| double | mu |
| double [] | mudt |
| 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 | sigma |
Detailed Description
Represents a geometric Brownian motion (GBM) process \(\{S(t), t\ge0\}\), which evolves according to the stochastic differential equation.
\[ dS(t) = \mu S(t) dt + \sigma S(t) dB(t), \tag{GBM} \]
where \(\mu\) and \(\sigma\) are the drift and volatility parameters, and \(\{B(t), t\ge0\}\) is a standard Brownian motion (for which \(B(t)\sim N(0,t)\)). This process can also be written as the exponential of a Brownian motion:
\[ S(t) = S(0) \exp\left[ (\mu- \sigma^2/2) t + \sigma B(t) \right] = S(0) \exp\left[ X(t) \right], \tag{GBM2} \]
where \(X(t) = (\mu- \sigma^2/2) t + \sigma B(t)\). The GBM process is simulated by simulating the BM process \(X\) and taking the exponential. This BM process is stored internally.
Constructor & Destructor Documentation
◆ GeometricBrownianMotion()
| GeometricBrownianMotion | ( | double | s0, |
| double | mu, | ||
| double | sigma, | ||
| BrownianMotion | bm | ||
| ) |
Constructs a new GeometricBrownianMotion with parameters \(\mu= \mathtt{mu}\), \(\sigma= \mathtt{sigma}\), and \(S(t_0) = \mathtt{s0}\), using bm as the underlying BrownianMotion.
The parameters of bm are automatically reset to \(\mu-\sigma^2/2\) and \(\sigma\), regardless of the original parameters of bm. The observation times are the same as those of bm. The generation method depends on that of bm (sequential, bridge sampling, PCA, etc.).
Member Function Documentation
◆ setParams()
| void setParams | ( | double | s0, |
| double | mu, | ||
| double | sigma | ||
| ) |
Sets the parameters \(S(t_0) = \mathtt{s0}\), \(\mu= \mathtt{mu}\) and \(\sigma= \mathtt{sigma}\) of the process.
Warning: This method will recompute some quantities stored internally, which may be slow if called repeatedly.
The documentation for this class was generated from the following file:
- GeometricBrownianMotion.java
