Stochastic variance models in discrete time with feedforward neural networks.

Area of Science:

• Quantitative Finance
• Computational Statistics
• Financial Econometrics

Background:

• Stochastic variance models are crucial for financial time series analysis but present estimation challenges.
• Accurate volatility estimation is essential for market risk assessment.
• Existing models may not fully leverage all available market information.

Purpose of the Study:

• To address the estimation difficulties in stochastic variance models for discrete financial time series.
• To develop a semiparametric method for volatility function estimation.
• To enhance market risk estimation by integrating time series data with supplementary market information.

Main Methods:

• Utilized feedforward neural networks for semiparametric estimation of the volatility function.
• Developed a novel approach to incorporate external market information alongside the primary time series.
• Applied the model to analyze and compare stock price series.

Main Results:

• Successfully overcame estimation difficulties in stochastic variance models.
• Demonstrated the effectiveness of the semiparametric neural network approach.
• The proposed model provides a more comprehensive market risk estimation compared to traditional methods like the nonlinear ARX-ARCHX model.

Conclusions:

• Feedforward neural networks offer a robust solution for estimating volatility in discrete financial time series.
• Incorporating additional market data significantly improves market risk assessment accuracy.
• The developed model represents an advancement in financial econometrics for risk management.