Entropy Based Student's t-Process Dynamical Model

Area of Science:

• Quantitative Finance
• Econometrics
• Statistical Modeling

Background:

• Volatility is crucial for asset allocation and derivative pricing but is unobservable.
• Conventional linear time-series models struggle with nonlinear and non-Gaussian volatility dynamics.
• Accurate volatility estimation is essential for financial risk management.

Purpose of the Study:

• To propose a novel volatility fluctuation model, the entropy-based Student's t-process Dynamical model (ETPDM).
• To incorporate nonlinear dynamics and non-Gaussian noise into volatility modeling.
• To enhance the estimation of unobservable volatility using advanced statistical methods.

Main Methods:

• Developed the entropy-based Student's t-process Dynamical model (ETPDM).
• Employed a robust particle filtering technique based on a generalized H-theorem for relative entropy.
• Estimated latent variables and intrinsic parameters of the ETPDM.

Main Results:

• The ETPDM successfully models both nonlinear dynamics and non-Gaussian noise in volatility.
• Numerical experiments on financial time-series validated the model's performance.
• The particle filtering approach demonstrated robustness even with a small number of particles.

Conclusions:

• The ETPDM offers a significant advancement over conventional linear models for volatility dynamics.
• The proposed method provides a robust framework for estimating unobservable financial volatility.
• This model has potential applications in improving asset allocation and derivative pricing.