Multivariate Stochastic Volatility Estimation with Sparse Grid Integration

Halil Erturk Esen

doi:10.4236/jmf.2016.61009

Abstract

Multivariate stochastic volatility (MSV) models are nonlinear state space models that require either linear approximations or computationally demanding methods for handling the high dimensional integrals arising in the estimation problems of the latent volatilities and model parameters. Markov Chain Monte Carlo (MCMC) methods, which are based on Monte Carlo simulations using special sampling schemes, are by far the most studied method with several extensions and versions in previous stochastic volatility estimation studies. Exact nonlinear filters and particularly numerical integration based methods, such as the method proposed in this paper, were neglected and not studied as extensively as MCMC methods especially in the multivariate settings of stochastic volatility models. Filtering, smoothing, prediction and parameter estimation algorithms based on the sparse grid integration method are developed and proposed for a general MSV model. The proposed algorithms for estimation are compared with an implementation of MCMC based algorithms in a simulation study followed by an illustration of the proposed algorithms on empirical data of foreign exchange rate returns of US dollars and Euro. Results showed that the proposed algorithms based on the sparse grid integration method can be promising alternatives to the MCMC based algorithms especially in practical applications with their appealing characteristics.

Highlights

Modeling, analysis, and estimation of volatilities of asset returns in financial markets have been a major researchHow to cite this paper: Esen, H.E. (2016) Multivariate Stochastic Volatility Estimation with Sparse Grid Integration
Comprehensive treatment of financial volatility and discussions on the stylized facts can be found in [1]-[4]
The goal of this paper is to show that the practical implementation of numerical integration method is possible by developing estimation algorithms incorporating the sparse grid integration methods as an alternative, and to depict that some important advantages of sparse grid integration methods over Markov Chain Monte Carlo (MCMC) methods can be realized for Multivariate stochastic volatility (MSV) models

Summary

Introduction

Analysis, and estimation of volatilities of asset returns in financial markets have been a major researchHow to cite this paper: Esen, H.E. (2016) Multivariate Stochastic Volatility Estimation with Sparse Grid Integration. Analysis, and estimation of volatilities of asset returns in financial markets have been a major research. (2016) Multivariate Stochastic Volatility Estimation with Sparse Grid Integration. Esen area in the last three decades because of the significant conceptual role of volatility in mathematical and quantitative finance. Reliable volatility estimates of asset returns are indispensible inputs to various mathematical models in financial frameworks including but not limited to risk management, option pricing, portfolio and asset management. A considerably rich literature on volatility research describes the well studied stylized facts about volatility including the time-varying nature of volatility, leverage effects, volatility spillovers, heavy tails and long memory. Comprehensive treatment of financial volatility and discussions on the stylized facts can be found in [1]-[4]

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