Bayesian Model Selection via Filtering for a Class of Micro-Movement Models of Asset Price

Abstract

This paper develops the Bayesian model selection based on Bayes factor for a rich class of partially-observed micro-movement models of asset price. We focus on one recursive algorithm to calculate the Bayes factors, first deriving the system of SDEs for them and then applying the Markov chain approximation method to yield a recursive algorithm. We prove the consistency (or robustness) of the recursive algorithm. To illustrate the construction of such a recursive algorithm, we consider a model selection problem for two micro-movement models with and without stochastic volatility, and provide simulation and real-data examples to demonstrate the effectiveness of the Bayes factor in the model selection for this class of models.

Bayesian Inference via Filtering for a Class of Counting Processes: Application to the Micromovement of Asset Price

“…The proof of Theorem 3.1 is in [13] and that of Theorem 3.2 is [9]. Note that a(t) disappears in equations (6), (9) and (10).…”

“…The proofs for (i) and (iii) are in [13] and those for (ii) and (iv) are in [9]. Another short proof of the whole theorem is provided in [14].…”

“…Alternatively, the price process can be constructed from the intrinsic value process by incorporating the trading noise. Zeng [13] also developed continuous-time Bayes parameter estimation via filtering for the model and Kouritzin and Zeng [9] further developed Bayesian model selection via filtering for the class of models based on Bayes factor.…”

Bayes estimation via filtering equation through implicit recursive algorithms for financial ultra-high frequency data

“…The above Thomas algorithm plus the updating equation (22) consist of the implicit recursive algorithm.…”

“…BEFE through explicit recursive algorithms has found successes of real-time Bayes estimation in models such as geometric Brownian motion (GBM) and jumping stochastic volatility among others for UHF stock prices when the tick size was 1/8 or 1/16 (that is, before the year of 2000). See, for example, [36], [34], [22], [35], and [30]. However, explicit recursive algorithms from BEFE suffer two curses when the tick size was reduced to 1/100 after the year of 2,000.…”