Refining value-at-risk estimates using a Bayesian Markov-switching GJR-GARCH copula-EVT model

In this paper, we propose a model for forecasting Value-at-Risk (VaR) using a Bayesian Markov-switching GJR-GARCH(1,1) model with skewed Student’s-t innovation, copula functions and extreme value theory. A Bayesian Markov-switching GJR-GARCH(1,1) model that identifies non-constant volatility over time and allows the GARCH parameters to vary over time following a Markov process, is combined with copula functions and EVT to formulate the Bayesian Markov-switching GJR-GARCH(1,1) copula-EVT VaR model, which is then used to forecast the level of risk on financial asset returns. We further propose a new method for threshold selection in EVT analysis, which we term the hybrid method. Empirical and back-testing results show that the proposed VaR models capture VaR reasonably well in periods of calm and in periods of crisis

Quasi-indirect inference for diffusion processes

We discuss an estimation procedure for continuous-time models based on discrete sampled data with a fixed unit of time between two consecutive observations. Because in general the conditional likelihood of the model cannot be derived, an indirect inference procedure following Gourieroux, Monfort, and Renault (1993, Journal of Applied Econometrics 8, 85-118) is developed, It is based on simulations of a discretized model. We study the asymptotic properties of this "quasi"-indirect estimator and examine some particular cases, Because this method critically depends on simulations, we pay particular attention to the appropriate choice of the simulation step. Finally, finite-sample properties are studied through Monte Carlo experiments

[Estimation of models of the term structure of interest rates]

We examine several estimation methods of one of the most useful instruments in interest rate risk management: the term structure of interest rates. We present mainly simulation-based methods al!owing for parametric estimation of continuous time models

Why Threshold Models: A Theoretical Explanation

Many economic phenomena are well described by linear models. In such models, the predicted value of the desired quantity -- e.g., the future value of an economic characteristic -- linearly depends on the current values of this and related economic characteristic and on the numerical values of external effects. Linear models have a clear economic interpretation: they correspond to situations when the overall effect does not depend, e.g., on whether we consider a loose federation as a single country or as several countries. While linear models are often reasonably accurate, to get more accurate predictions, we need to take into account that real-life processes are nonlinear. To take this nonlinearity into account, economists use piece-wise linear (threshold) models, in which we have several different linear dependencies in different domains. Surprisingly, such piece-wise linear models often work better than more traditional models of non-linearity -- e.g., models that take quadratic terms into account. In this paper, we provide a theoretical explanation for this empirical success of threshold models

Modelling Asymmetric Behaviour in Time Series: Identification Through PSO

In this work we propose an estimation procedure of a specific TAR model in which the actual regime changes depending on both the past value and the specific past regime of the series. In particular we consider a system that switches between two regimes, each of which is a linear autoregressive of order p. The switching rule, which drives the process from one regime to another one, depends on the value assumed by a delayed variable compared with only one threshold, with the peculiarity that even the thresholds change according to the regime in which the system lies at time t -d. This allows the model to take into account the possible asymmetric behaviour typical of some financial time series. The identification procedure is based on the Particle Swarm Optimization technique

The adjustments of stock prices to information about inflation: evidence from MENA countries

This study extends the empirical evidence by analysing the reaction of monthly stock returns to the unexpected portion of CPI inflation rate and by capturing the asymmetric shocks to volatility of unexpected inflation in five MENA countries. Both Threshold GARCH and Exponential GARCH are used to catch the news affect that unexpected inflation may have on stock returns. Results document a negative and strongly significant relationship between unexpected inflation and stock returns in MENA countries. Results also indicate that the stock markets of the listed MENA countries do not feel the high up and down movements in the markets and as such the volatilities. The asymmetric news effect is absent.