Fractional processes and their financial applications
Team:
Daniel Boros, Ivan Ivkovic, Laszlo Markus
Student level:
PhD
Our research focuses on stochastic processes with fractional properties and their application in finance. Typical examples include the fractional Brownian motion and fractional Ornstein-Uhlenbeck processes. A crucial part of our research is the accurate estimation of process parameters, for instance the Hurst parameter, which determines the "memory" of the process. In the literature, estimates based on fractal dimensions proved to be the most accurate for these processes.
Our goal is to provide even more accurate estimates using neural networks. We implemented a statistical framework in Python capable of quickly and accurately producing these processes in large quantities, and test whether we indeed generate the correct processes. Our Python engine can serve as a benchmark for neural networks, making it easy to compare the performance of different approaches. The developed neural network showes promising results in terms of both accuracy and speed. It provides an estimate at least an order of magnitude more accurate than traditional statistical methods and it is also much faster.
In the next phase, our plan is to thoroughly examine the stochastic correlation features of the Heston model, and expand our previous neural network results to fractional Cox-Ingersoll-Ross (CIR) and Jacobi processes. The Heston model is of fundamental importance in financial analysis, especially in derivative pricing, as this model allows for modeling the stochastic dynamics of price volatility. The introduction of stochastic correlation into the model provides an even finer tool for modeling the complex dynamics of financial markets, thereby enabling more accurate pricing and risk management strategies.
Incorporating fractional CIR and Jacobi processes into the research opens up new dimensions. These processes allow for the modeling of long-memory properties, i.e., the long-term effects of past events, which are often present in financial markets. Proper modeling of these processes and accurate estimation of their parameters can help in better forecasting future behavior of financial markets thus greatly contributing to improving financial decision-making.
Alongside theoretical research we place strong emphasis on the practical applications of these models. We do comparative analysis of the performance of our models against current market approaches, and explore the applicability of our models in pricing financial instruments and developing risk management strategies.
Our research focuses on stochastic processes with fractional properties and their application in finance. Typical examples include the fractional Brownian motion and fractional Ornstein-Uhlenbeck processes. A crucial part of our research is the accurate estimation of process parameters, for instance the Hurst parameter, which determines the "memory" of the process. In the literature, estimates based on fractal dimensions proved to be the most accurate for these processes.
Our goal is to provide even more accurate estimates using neural networks. We implemented a statistical framework in Python capable of quickly and accurately producing these processes in large quantities, and test whether we indeed generate the correct processes. Our Python engine can serve as a benchmark for neural networks, making it easy to compare the performance of different approaches. The developed neural network showes promising results in terms of both accuracy and speed. It provides an estimate at least an order of magnitude more accurate than traditional statistical methods and it is also much faster.
In the next phase, our plan is to thoroughly examine the stochastic correlation features of the Heston model, and expand our previous neural network results to fractional Cox-Ingersoll-Ross (CIR) and Jacobi processes. The Heston model is of fundamental importance in financial analysis, especially in derivative pricing, as this model allows for modeling the stochastic dynamics of price volatility. The introduction of stochastic correlation into the model provides an even finer tool for modeling the complex dynamics of financial markets, thereby enabling more accurate pricing and risk management strategies.
Incorporating fractional CIR and Jacobi processes into the research opens up new dimensions. These processes allow for the modeling of long-memory properties, i.e., the long-term effects of past events, which are often present in financial markets. Proper modeling of these processes and accurate estimation of their parameters can help in better forecasting future behavior of financial markets thus greatly contributing to improving financial decision-making.
Alongside theoretical research we place strong emphasis on the practical applications of these models. We do comparative analysis of the performance of our models against current market approaches, and explore the applicability of our models in pricing financial instruments and developing risk management strategies.