Non-Gaussian Stochastic Volatility Model with Jumps via Gibbs Sampler

Abstract

To understand the behavior of asset prices is essential for capital allocation decisions between the available investment option. Such decision depends on what one thinks about risks and returns associated with these investment options. On the literature there are models focused on estimating financial assets risk, however, most of them depend on MCMC methods based on Metropolis algorithms, which makes them computationally expensive. This work presents an alternative model, the Non Gaussian Stochastic Volatility Model with Jumps (NGSVJ), based on the Dynamic Linear Model (DLM) with mixture, capable of estimating the volatility without appealing to intensive computational methods, using only Gibbs Sampler. This is possible due to the model structure, which allows the posterior full conditionals for parameters. Besides that, the insertion of jumps on modeling the returns allows it to capture isolated speculative movements of the market, without transferring its effects to volatility. Simulated studies are presented in order to investigate the efficiency of the proposed method. Finally, an analysis with real data is performed using return series from S&P 500 and iBovespa indexes. Results indicate that the proposed model was capable of estimating volatility, with results similar to other models on literature, in a computationally efficient and automated way, being that its ability to identify jumps is greater when the series of returns under study has strong speculative movements. A non-parametric method was also used for estimating jumps, but simulation results showed that it was not effective