.NET Stochastic Volatility Models

Based on some conversations with others on the use of 3rd party products, I have been putting the materials together for building C++.NET or C#.NET algorithms for Stochastic Volatility models (SVM) for my paper. In the course of my research, I came across the following open source application at Carnegie-Mellon for doing time series analysis.

http://www.stat.cmu.edu/~abrock/cronos/index.html

I downloaded the software as well as the source for modifying the C++ algorithms based on the open source thread safe GSL-GNU scientific library at

http://www.gnu.org/software/gsl/

for the optimization routines. Of course, I have to ramp-up to be able to implement them in Visual Studio 2008 C++ or C# Express, but should be able to accomplish that this month. Here is an example of the SVM code for the svm.h file:


/*
* -------------------------------------------------------------------
*
* Copyright 2005 Anthony Brockwell
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Library General Public
* License as published by the Free Software Foundation; either
* version 2 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Library General Public License for more details.
*
* You should have received a copy of the GNU Library General Public
* License along with this library; if not, write to the Free
* Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*
* -------------------------------------------------------------------
*/
#ifndef SVM_H
#define SVM_H
// simple stochastic volatility model first
// Y_t \sim N(\mu_Y,\sigma_t^2)
// \sigma_t = \exp(X_t + \mu_X)
// X_t = \phi X_{t-1} + \epsilon_t, {\epsilon_t} \sim IIDN(0,\nu^2)
class SSVModel : public TimeSeriesModel {
protected:
double mean, mux, phi, nu;

public:
SSVModel(); // constructor
int FitModel(TimeSeries *ts, const int method, const int ilimit,
void (*itercallback)(int,void *), void *cb_parms,
ostringstream& msg, ostringstream& supplementalinfo,
bool get_parameter_cov=true);
void SimulateInto(TimeSeries *, int n, bool ovw);
Matrix SimulatePredictive(TimeSeries&, int nsteps, int nsims);
void RenderInto(ostringstream&);
bool RenderCtsVersionInto(ostringstream &output, ostringstream &error, double delta);
void ComputeACFPACF(Vector &acf, Vector *pacf, bool normalizeacf=true);
void Forecast(TimeSeries *, int nsteps, double *fret, double *fmse);
void ComputeStdResiduals(TimeSeries *data, TimeSeries *resids);
double ComputeLogLikelihood(TimeSeries *);
bool CheckModel(bool flipit);
Vector ParameterBundle();
void UnbundleParameters(Vector& v);
Vector ValidityConstraint();
Vector GetMask(); // returns estimation_mask, padded with defaults
Vector GetDefaultParameters(Vector& mask, TimeSeries *tsp); // returns initial guesses for non-held model parameters; other parameters are fixed at current values
void StreamParameterName(ostringstream& strm, int parmnum); // nms[0],... must already be valid allocated strings with length >= 20
Vector ComputeSpectralDensity(Vector& omegas);
double Cdf(double y, double mu, double sig2);
double InvCdf(double u, double mu, double sig2);
};
#endif


I used the Cronos application to estimate a SVM model and some forecasting as shown in Figure 2. Next, step is to show the use of the application and discuss time series analysis in a video.

Figure 2.

To learn more about Stochastic Volatility models, a good place to start is the presentation by Peter Jackel

http://www-stat.wharton.upenn.edu/~steele/Courses/95/ResourceDetails/SV/StochasticVolatilityModels-PastPresentAndFuture.pdf

The next step in this continued research on algorithmic trading is to review the C++ architecture for doing a SVM in the context of the algorithmic trading architecture-so I can finish my paper and discuss some of my observations along the way.