Projects

Portfolio optimization in a fractional Black-Scholes market

People:

• University of Southern Indiana, Mathematics Department: Professor Yalcin Sarol
• Purdue University, Mathematics Department: Mr. Tao Zhang
• Purdue University, Statistics Department: Professor Frederi G. Viens

Publication: Portfolio optimization with consumption in a fractional Black-Scholes market. Preprint, 2006. With Y. Sarol, T. Zhang.

 

Option pricing under partially observed stochastic volatility

People:

• Stevens Institute of Technology, NJ, Mathematics Department: Professor Ionut Florescu
• Purdue University, Statistics Department: Professor Frederi G. Viens

Publication:
A Binomial Tree Approach to Stochastic Volatility Driven Model of the Stock Price. Annals of the University of Craiova, Mathematics and Computer Science Series, 32 (2005), p. 126-142.

 

Portfolio optimization under partially observed stochastic volatility

People:

• Bank of America Securities, London, UK: Dr. Natalia Batalova
• Purdue University, Chemistry Department: Mr. Tanmay Lele
• Purdue University, Mathematics Department: Mr. Rahul Desai
• Purdue University, Mathematics Department: Mr. Andrew B. Vizcarra
• Purdue University, Physics Department: Mr. Vassili Maroussov
• Purdue University, Statistics Department: Professor Frederi G. Viens

Publications:

Portfolio optimization under partially observed stochastic volatility. COMCON 8. The 8th International Conference on Advances in Communication and Control. W. Wells, Ed. 1-12. Optim. Soft., Inc, Pub. Div., 2002.

A Monte-Carlo method for portfolio optimization under partially observed stochastic volatility. IEEE International Conference on Computational Intelligence for Financial Engineering, 2003. Proceedings (2003), 257 - 263. With R. Desai and T. Lele.

Selection of an Optimal Portfolio with Stochastic Volatility and Discrete Observations. Transactions of the Wessex Institute on Modelling and Simulation, 43 (2006), 371-380. With N. Batalova and V. Maroussov.

 

Hurst parameter estimation for fractional Brownian motion and ARCH models.

People:

• Purdue University, Statistics Department: Professor Michael Levine
• Universidad de Valparaiso, Chile, Estadistica/CIMFAV: Professor Soledad Torres
• Purdue University, Statistics Department: Professor Frederi G. Viens

Description:

Time series data for financial returns is typically uncorrelated with but with heavy dependence of long range type. While it has been understood for several years that such time series bears a strong connection with the fractional Brownian motion (fBm), here we show that this connection can be explained using a simple coupling argument, not just a mere convergence in distribution, and that this coupling can be the basis for an estimation scheme for the fBm's Hurst parameter, using a specific ARCH model's conditional maximum likelihood estimator.

 

Portfolio optimization in Levy markets.

People:

• Purdue University, Statistics Department: Professor Jose E. Figueroa-Lopez
• University of Southern California, Department of Mathematics: Professor Jin Ma

 

Statistical methods for asset price models driven by Levy processes.

People:

Purdue University, Statistics Department: Professor Jose E. Figueroa-Lopez

 

Calibration of credit models driven by continuous time Markov processes.

People:

• Purdue University, Statistics Department: Professor Jose E. Figueroa-Lopez
• Purdue University, School of Industrial Engineering: Shaunak Dabadghao

 

Nonparametric financial volatility models.

People:

• Purdue University, Statistics Department: Professor Michael Levine
• Canadian Pension Fund, Dr. Tony (Jinguang) Li