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

Stat Inference Stoch Process

2011

Self Cite

Section: Assumptionmentioning

confidence: 88%

“…Examples of F(x)(or p(y|x; t)) are given in Zeng (2003) and Zeng (2005). These examples well accommodate the three types of well-documented noise in financial literature: discrete noise, clustering noise, and non-clustering noise.…”

Section: Assumptionmentioning

confidence: 88%

A branching particle approximation to a filtering micromovement model of asset price

Xiong

Stat Inference Stoch Process

2011

Self Cite

“…The equivalence ensures that the statistical analysis based on the latter specification can be applied to the former and the equivalence is proven by Zeng (2005).…”

Section: Representation Ii: Filtering With Counting Process Observationsmentioning

confidence: 94%

Risk Minimization for a Filtering Micromovement Model of Asset Price

Lee

Applied Mathematical Finance

2010

Self Cite

The classical option hedging problems have mostly been studied under continuous-time or equally spaced discrete-time models, which ignore two important components in the actual price: random trading times and market microstructure noise. In this paper, we study optimal hedging strategies for European derivatives based on a filtering micromovement model of asset prices with the two commonly ignored characteristics. We employ the local risk-minimization criterion to develop optimal hedging strategies under full information. Then, we project the hedging strategies on the observed information to obtain hedging strategies under partial information. Furthermore, we develop a related nonlinear filtering technique under the minimal martingale measure for the computation of such hedging strategies.Risk minimization, Minimal martingale measure, Filtering, Counting process, High frequency data,

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Bundick

Rhee

Statistics and Its Interface

2013

Self Cite

We review a recently proposed general partially-observed framework of Markov processes with marked point process observations for financial ultra-high frequency (UHF) data, and the related Bayes estimation via filtering equation (BEFE), a stochastic PDE approach. In this paper, we show how the BEFE through explicit recursive algorithms becomes bottlenecked when the tick size is reduced from $1/8 to $1/100, and we develop the BEFE through implicit recursive algorithms, greatly improving the computational efficiency. We demonstrate the substantial computation gained in implementing real-time BEFE for an illustrating but practical model using simulated data. The new implicit recursive algorithm is applied to a real stock price UHF data set, and is capable of producing real time Bayes parameter estimates of the model. AMS 2000 subject classifications: Primary 62M05, 62F15, 62P05; secondary 60H35, 60G55, 65C60, 93E11.