Estimation and filtering by reversible jump MCMC for a doubly stochastic Poisson model for ultra-high-frequency financial data

Abstract

We propose a modeling framework for ultra-high-frequency data on financial asset price movements. The models proposed belong to the class of the doubly stochastic Poisson processes with marks and allow an interpretation of the changes in price volatility and trading activity in terms of news or information arrival. Assuming that the intensity process underlying event arrivals is unobserved by market agents, we propose a signal extraction (filtering) method based on the reversible jump Markov chain Monte Carlo algorithm. Moreover, given a realization of the price process, inference on the parameters can be performed by appealing to stochastic versions of the expectation-maximization algorithm. The simulation methods proposed will be applied to the computation of hedging strategies and derivative prices.

Monte Carlo Filtering of Piecewise Deterministic Processes

“…The method we propose suffers from no such restrictions. Similar models find applications in the pricing of options; see, for example, the article by Centanni and Minozzo (2006).…”

“…Exact inference for SNCP models is intractable. Approximate methods based on weak convergence to Gaussian processes in specific parameter regimes (Dassios and Jang 2005) and Markov chain Monte Carlo have been proposed (Centanni and Minozzo 2006).…”

Filtering on a Partially Observed Ultra-High-Frequency Data Model

“…In this paper, we propose a model following in some sense the same line of that presented in [7], adding a Markovianity assumption. Our model is presented in Section 2, where we assume that the unobservable latent process X t is a marked point process.…”

“…In [7], as suggested by the economic literature, the authors take explicitly into account the link between the information released and the changes in the price volatility and trading activity. Essentially, we focus on this last paper, in which the process N t , counting the number of the variations of the observed prices up to time t, has an intensity that increases once a piece of news reaches the market, of a quantity depending on its importance.…”

Stochastic Control Methods: Hedging in a Market Described by Pure Jump Processes

“…Several models in which a jumping behavior of the price process is allowed are also available in the literature, related to different problems, in addition to [29] we only quote [6,10,11,14,15,18,27,28] and the references therein.…”