Volatility estimation via hidden Markov models

Abstract

We propose a stochastic volatility model where the conditional variance of asset returns switches across a potentially large number of discrete levels, and the dynamics of the switches are driven by a latent Markov chain. A simple parameterization overcomes the commonly encountered problem in Markov-switching models that the number of parameters becomes unmanageable when the number of states in the Markov chain increases. This framework presents some interesting features in modelling the persistence of volatility, and that, far from being constraining in data fitting, it performs comparably well as other popular approaches in forecasting short-term volatility.

Clustering financial time series: New insights from an extended hidden Markov model

“…There is a vast body of literature on RSMs in economics and empirical finance, including Hamilton (1989), Susmel (1994), andGray (1996) to name just a few. Hidden Markov models and regime-switching models as discrete state models can also be connected to stochastic volatility models (see, e.g., Rossi and Gallo (2006) and Langrock et al (2012)). The autoregressive conditional root (ACR) model (Bec et al, 2008) is another econometric model that connects to regime-switching models.…”

Some nonstandard stochastic volatility models and their estimation using structured hidden Markov models

“…A different approach to the use of HMMs as models for share returns is that of Rossi and Gallo (2006). Unlike our work, theirs does not seek to approximate (standard or non-standard) SV models, which have a continuous-valued latent process.…”

A Stochastic Context-Free Grammar Model for Time Series Analysis

“…However, these models tend to have long memory and sometimes fail to accurately track abrupt changes in market conditions. Hidden Markov models (HMMs) which have been widely used in signal processing for a long time-especially in speech analysis and recognition [13]-have been recently suggested to improve modeling of market changes [5,14]. Specically, several HMM-based approaches have been proposed to model the fact that typically high-volatility periods are shorter than lowvolatility periods.…”

“…In [8], a regime-switching volatility model is proposed where different regimes correspond to different volatility levels. Other models have been proposed where the volatility process is assumed to be generated by a hidden nite-state Markov process [5,14]. In addition, the framework of [14] models the leverage effect, i.e., the empirical observation that negative returns typically lead to higher volatility than positive returns.…”

“…Other models have been proposed where the volatility process is assumed to be generated by a hidden nite-state Markov process [5,14]. In addition, the framework of [14] models the leverage effect, i.e., the empirical observation that negative returns typically lead to higher volatility than positive returns. Variants of GARCH that model the leverage effect are proposed in [7] and [16].…”