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Entropy Based Student's t-Process Dynamical Model.

Ayumu Nono1, Yusuke Uchiyama2, Kei Nakagawa3

  • 1Graduated School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

Entropy (Basel, Switzerland)
|May 5, 2021
PubMed
Summary
This summary is machine-generated.

We introduce a new financial model, the entropy-based Student's t-process Dynamical model (ETPDM), to better capture complex volatility dynamics. This model effectively handles nonlinear and non-Gaussian properties, improving financial forecasting and risk management.

Keywords:
Student’s t-processentropy based particle filterfinancerelative entropyvolatility fluctuation

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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.