A Multivariate Stochastic Volatility Model for Portfolio Risk Estimation

2014 ◽  
pp. 197-206
Author(s):  
Andrea Pierini ◽  
Antonello Maruotti
Keyword(s):  
Stochastic Volatility ◽  
Risk Estimation ◽  
Stochastic Volatility Model ◽  
Portfolio Risk ◽  
Volatility Model ◽  
Multivariate Stochastic Volatility

scholarly journals Cross-Commodity Spot Price Modeling with Stochastic Volatility and Leverage For Energy Markets

2013 ◽  
Vol 45 (02) ◽  
pp. 545-571 ◽  
Author(s):  
F. E. Benth ◽  
L. Vos
Keyword(s):  
Stochastic Volatility ◽  
Simulation Method ◽  
Energy Markets ◽  
Stochastic Volatility Model ◽  
Spot Price ◽  
Leverage Effect ◽  
Order Structure ◽  
Spot Prices ◽  
Volatility Model ◽  
Multivariate Stochastic Volatility

Spot prices in energy markets exhibit special features, such as price spikes, mean reversion, stochastic volatility, inverse leverage effect, and dependencies between the commodities. In this paper a multivariate stochastic volatility model is introduced which captures these features. The second-order structure and stationarity of the model are analyzed in detail. A simulation method for Monte Carlo generation of price paths is introduced and a numerical example is presented.

scholarly journals Dynamic Correlation Multivariate Stochastic Volatility Black-Litterman With Latent Factors

2021 ◽  
Vol 10 (2) ◽  
pp. 1
Author(s):  
Mihnea S. Andrei ◽  
Sujit K. Ghosh ◽  
Jian Zou
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Mcmc Algorithm ◽  
Latent Factors ◽  
Dynamic Correlation ◽  
Confidence Levels ◽  
Volatility Models ◽  
Volatility Model ◽  
Multivariate Stochastic Volatility ◽  
Modeling Volatility

In finance, it is often of interest to study market volatility for portfolios that may consist of a large number of assets using multivariate stochastic volatility models. However, such models, though useful, do not usually incorporate investor views that might be available. In this paper we introduce a novel hierarchical Bayesian methodology of modeling volatility for a large portfolio of assets that incorporates investor’s personal views of the market via the Black-Litterman (BL) model. We extend the scope and use of BL models by using it within a multivariate stochastic volatility model based on latent factors for dimensionality reduction but allows for time varying correlations. Detailed derivations of MCMC algorithm are provided with an illustration with S&P500 asset returns. Moreover, sensitivity analysis for the confidence levels that the investor has in their personal views is also explored. Numerical results show that the proposed method provides flexible interpretation based on the investor’s uncertainty in personal beliefs, and converges to the empirical sample estimate when their confidence level of the market becomes weak.

scholarly journals “Exact” and Approximate Methods for Bayesian Inference: Stochastic Volatility Case Study

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 466
Author(s):  
Yuliya Shapovalova
Keyword(s):  
Bayesian Inference ◽  
Stochastic Volatility ◽  
Particle Filtering ◽  
Point Of View ◽  
Stochastic Volatility Model ◽  
Approximate Methods ◽  
Volatility Model ◽  
Multivariate Stochastic Volatility ◽  
Important Practical Application

We conduct a case study in which we empirically illustrate the performance of different classes of Bayesian inference methods to estimate stochastic volatility models. In particular, we consider how different particle filtering methods affect the variance of the estimated likelihood. We review and compare particle Markov Chain Monte Carlo (MCMC), RMHMC, fixed-form variational Bayes, and integrated nested Laplace approximation to estimate the posterior distribution of the parameters. Additionally, we conduct the review from the point of view of whether these methods are (1) easily adaptable to different model specifications; (2) adaptable to higher dimensions of the model in a straightforward way; (3) feasible in the multivariate case. We show that when using the stochastic volatility model for methods comparison, various data-generating processes have to be considered to make a fair assessment of the methods. Finally, we present a challenging specification of the multivariate stochastic volatility model, which is rarely used to illustrate the methods but constitutes an important practical application.

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