Leitura do Dia - Estimating Stochastic Volatility Models Using Integrated Nested Laplace Approximations

Estimating Stochastic Volatility Models Using Integrated Nested Laplace Approximations

Sara Martino(1), Kjersti Aas(2), Ola Lindqvist(2) , Linda Reiersølmoen Neef(2) & Havard Rue(1)

(1) Department of Mathematical Science, NTNU, Norway
(2) Norwegian Computing Center, Oslo, Norway
Abstract
Volatility in financial time series is mainly analysed through two classes of models; the Generalised Autoregressive Conditional Heteroscedasticity (GARCH) models and the Stochastic Volatility (SV) ones. GARCH models are straight-forward to estimate using maximum likelihood techniques, while SV models require more complex inferential and computational tools, like Markov Chains Monte Carlo (MCMC).
Hence, although provided with a series of theoretical advantages, SV models are in practice much less popular than GARCH ones. In this paper we solve the problem of inference for some SV models by applying a new inferential tool, Integrated Nested Laplace Approximations (INLA), which substitutes MCMC simulations with accurate deterministic approximations, making a full Bayesian analysis of many kinds of SV models extremely fast and accurate. Our hope is that the use of INLA will help SV models to become more appealing to the financial industry where, due to their complexity, they are rarely used in practice.

Keywords
Approximate Bayesian Inference, Laplace Approximation, Latent Gaussian Models, Stochastic Volatility Model.


A apresentação do Havard Rue no EBEB foi a que eu achei mais interessante. Os ganhos de eficiência do INLA, são para dizer o mínimo, brutais. No caso de estimação de modelos SV por MCMC, os ganhos são realmente extraordinários e tornam a estimação de SV quase tão simples quanto a de modelos GARCH.