A Partially Observed Merton’s Jump Model for Ultra-High Frequency Financial Data with Bayesian Learn

Oregon Convention Center 

The time-stamped transactions financial data, which possess the most detailed information for price evolution, are coined as "ultrahigh-frequency (UHF) data" in Engle (2000). A general partially observed Markov process framework with marked point observations and the related Bayesian inference (estimation and model selection) via stochastic filtering equations are developed in Hu, Kuipers, and Zeng (2018a and 2018b). The general framework accommodates the two features of UHF data: random trading times and trading noises. While several specific partially observed models, including the Black-Scholes (BS) and stochastic volatility models, have been studied, the partially observed Merton's model, extending the BS model with a jump component representing the impact of good and bad news, has not been investigated. In this study, we fill such a gap by proposing a partially observed Merton's model for ultra-high frequency financial data, accommodating the two UHF-data features. The joint posterior distribution of the parameters of interest and the intrinsic value process (which is the Merton model) is characterized by the normalized filtering equation. The Bayes factors of the partially ob

Ultrahigh-frequency data

Partially observed Merton’s jump model

Normalized filtering equation

Bayes factors 

Business and Economic Statistics Section