A Bayesian Approach to Risk Management in a World of High-Frequency Data

A Realised Volatility GARCH model using high-frequency data is developed within a Bayesian framework for the purpose of forecasting Value at Risk and Conditional Value at Risk. A Skewed Student-t return distribution is combined with a Student-t distribution in the measurement equation in a GARCH framework. Realised Volatility GARCH models show a marked improvement compared to ordinary GARCH. A Skewed Student-t Realised DCC copula model using Realised Volatility GARCH marginal functions is developed within a Bayesian framework for the purpose of forecasting portfolio tail risk. The use of copulas is implemented so that the marginal distributions can be separated from the dependence structure to produce tail forecasts. This is compared to using traditional GARCH-copula models, and GARCH on an aggregated portfolio. Copula models implementing a Realised Volatility GARCH framework show an improvement over traditional GARCH models. A Bayesian detection of regime changes utilizing high-frequency data is developed, once again for the purpose of forecasting portfolio tail risk. The use of high-frequency data improves the accuracy of regime change detection compared to daily data. Monte Carlo sampling schemes are employed for the estimation of these models

Međusobna ovisnost hrvatskog i pojedinih europskih dioničkih tržišta – Kopula GARCH pristup

The objective of this paper is to analyze dependence structure between the returns of Croatian and five European stock markets (Austrian, French, German, Italian, and the U.K.’s). We propose a copula GARCH approach, where the return series are modeled as univariate GARCH processes and the dependence structure between the return series is defined by a copula function. Four different copulas are fitted – a constant and conditional normal and symmetric Joe-Clayton (SJC) copulas – and estimated by a semi-parametric method. We found that the time-varying normal copula yields the best fit for CROBEX-CAC40, CROBEX-DAX, and CROBEX-FTSE-MIB stock indices pairs, while the time-varying SJC copula is the best fit for CROBEX-ATX and CROBEX-FTSE100. Further, we found that the probability of simultaneous extreme positive and negative returns in Croatian and other European stock markets can increase to 0.77 during turbulent times. The lower and upper tail dependence dynamics between Croatian and other European stock markets is similar in pattern, differing only in scale. The basic conclusion of the research is that the dependence between the stock markets of Croatia and five major European stock markets is dynamic and can be properly captured by either a dynamic normal or symmetrized Joe-Clayton copula GARCH models.Cilj ovog rada je analizirati strukturu međusobne ovisnosti prinosa hrvatskog i pet europskih dioničkih tržišta (austrijskog, francuskog, njemačkog, talijanskog i britanskog). Ishodišna hipoteza jest, da je međusobna ovisnost dinamična i vjerojatno nelinearna i stoga ne može biti korektno ocjenjena primjenom običnih mjera međuzavisnosti, kao što su Pearsonova korelacija i dinamična korelacija. Umjesto toga, u ovom se radu primjenjuje pristup kopula GARCH, s univarijantnim GARCH modeliranjem prinosa pojedinih tržišta, a struktura međusobne ovisnosti modelira se kopula funkcijama. Upotrijebljene su četiri različite kopula funkcije – konstantna i kondicionalna normalna i simetrična Joe-Claytonova (SJC) kopula – koje se ocjenjuju semi-parametričnom metodom. Rezultati studije pokazuju, da najbolju ocjenu međusobne ovisnosti između indeksa CROBEX-CAC40, CROBEX-DAX i CROBEX-FTSEMIB pruža dinamična normalna kopula, a između CROBEX-ATX i CROBEX-FTSE100 dinamična SJC kopula. Jedan od rezultata ove studije ukazuje na to da vjerojatnost simultanog ekstremnog pozitivnog i ekstremno negativnog prinosa na hrvatskom i jednom od drugih istraženih europskih dioničkih tržišta može porasti na 77 % u trenutku ekstremne volatilnosti na dioničkom tržištu

Improved Bayesian Multi-Modeling: Integration of Copulas and Bayesian Model Averaging

Bayesian Model Averaging (BMA) is a popular approach to combine hydrologic forecasts from individual models, and characterize the uncertainty induced by model structure. In the original form of BMA, the conditional probability density function (PDF) of each model is assumed to be a particular probability distribution (e.g. Gaussian, gamma, etc.). If the predictions of any hydrologic model do not follow certain distribution, a data transformation procedure is required prior to model averaging. Moreover, it is strongly recommended to apply BMA on unbiased forecasts, whereas it is sometimes difficult to effectively remove bias from the predictions of complex hydrologic models. To overcome these limitations, we develop an approach to integrate a group of multivariate functions, the so-called copula functions, into BMA. Here, we introduce a copula-embedded BMA (Cop-BMA) method that relaxes any assumption on the shape of conditional PDFs. Copula functions have a flexible structure and do not restrict the shape of posterior distributions. Furthermore, copulas are effective tools in removing bias from hydrologic forecasts. To compare the performance of BMA with Cop-BMA, they are applied to hydrologic forecasts from different rainfall-runoff and land-surface models. We consider the streamflow observation and simulations for ten river basins provided by the Model Parameter Estimation Experiment (MOPEX) project. Results demonstrate that the predictive distributions are more accurate and reliable, less biased, and more confident with small uncertainty after Cop-BMA application. It is also shown that the post-processed forecasts have better correlation with observation after Cop-BMA application

Estimation of a microfounded herding model on German survey expectations

The paper considers the dynamic adjustments of an average opinion index that can be derived from a microfounded framework where the individual agents switch between two kinds of sentiment with certain transition probabilities. The index can thus represent a general business climate, i.e., expectations about the future course of the economy. This approach is empirically tested with the survey expectations published by the ZEW and ifo institute. The estimated coefficients make economic sense and are highly significant. In particular, besides effects from fundamental data like the output gap in the recent past, one can identify a strong herding mechanism within both panels, such that metaphorically speaking the agents do not just join the crowd but follow each single motion of it. In addition, the transition probabilities of the ZEW agents are found to be influenced by the ifo climate but not the other way round

Improved Bayesian multimodeling: Integration of copulas and Bayesian model averaging

Bayesian Model Averaging (BMA) is a popular approach to combine hydrologic forecasts from individual models, and characterize the uncertainty induced by model structure. In the original form of BMA, the conditional probability density function (PDF) of each model is assumed to be a particular probability distribution (e.g. Gaussian, gamma, etc.). If the predictions of any hydrologic model do not follow certain distribution, a data transformation procedure is required prior to model averaging. Moreover, it is strongly recommended to apply BMA on unbiased forecasts, whereas it is sometimes difficult to effectively remove bias from the predictions of complex hydrologic models. To overcome these limitations, we develop an approach to integrate a group of multivariate functions, the so-called copula functions, into BMA. Here, we introduce a copula-embedded BMA (Cop-BMA) method that relaxes any assumption on the shape of conditional PDFs. Copula functions have a flexible structure and do not restrict the shape of posterior distributions. Furthermore, copulas are effective tools in removing bias from hydrologic forecasts. To compare the performance of BMA with Cop-BMA, they are applied to hydrologic forecasts from different rainfall-runoff and land-surface models. We consider the streamflow observation and simulations for ten river basins provided by the Model Parameter Estimation Experiment (MOPEX) project. Results demonstrate that the predictive distributions are more accurate and reliable, less biased, and more confident with small uncertainty after Cop-BMA application. It is also shown that the post-processed forecasts have better correlation with observation after Cop-BMA application