Sequential Bayesian Learning for Merton's Jump Model with Stochastic Volatility

TL;DR

This paper introduces a particle filtering method for sequentially estimating volatility and jump parameters in Merton's jump stochastic volatility model, enabling real-time updates crucial for financial decision-making.

Contribution

It develops a novel particle filtering algorithm that allows for efficient sequential learning of volatility and jump parameters in complex stochastic models.

Findings

Successfully applied to Google's stock data

Enables real-time filtering of volatility and jump times

Provides a practical tool for financial econometrics

Abstract

Jump stochastic volatility models are central to financial econometrics for volatility forecasting, portfolio risk management, and derivatives pricing. Markov Chain Monte Carlo (MCMC) algorithms are computationally unfeasible for the sequential learning of volatility state variables and parameters, whereby the investor must update all posterior and predictive densities as new information arrives. We develop a particle filtering and learning algorithm to sample posterior distribution in Merton's jump stochastic volatility. This allows to filter spot volatilities and jump times, together with sequentially updating (learning) of jump and volatility parameters. We illustrate our methodology on Google's stock return. We conclude with directions for future research.