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|Title:||Bayesian Methods for Estimation, Inference and Forecasting of Flexible Models for Value-at-Risk and Tail Conditional Expectations|
|Keywords:||Bayesian method, Value-at-Risk, expected shortfall, asymmetric Laplace, two-sided Weibull, partitioned distribution,backtesting, Markov chain Monte Carlo, mixture of Gaussian, financial crisis, risk measurement, conditional tail expectation|
|Publisher:||University of Sydney.|
|Abstract:||Forecasting financial risk and risk measurement methods have been of increasing interest for financial market regulators and financial institutions in the past two decades. While the parametric and semi-parametric models have been widely reviewed in the academic literature, the non-parametric methods are popular in practice among the financial institutions. This thesis examines the forecasting models for Value-at-Risk (VaR) and conditional Value-at-Risk for financial return series. The aims of this thesis are to: 1. Estimate and forecast the potential skewness and dynamics in higher moments for conditional return distributions; 2. Develop flexible parametric models that can accurately forecast the portfolio tail risk levels. 3. Examine the impacts of asymmetry in the volatility and that in the shape of the conditional return distributions on the risk level forecasting. 4. Derive an easily applicable backtesting method for conditional VaR or expected shortfall. 5. Improve the efficiency and accuracy of Bayesian computational schemes for parameter estimation and forecasts. To achieve the above goals, this thesis first proposes a parametric approach to estimating and forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) for a heteroscedastic financial return series. A GJR-GARCH is used to model the volatility process, capturing the leverage effect. To account for potential skewness and heavy tails, the model assumes an asymmetric Laplace (AL) distribution as the conditional distribution of the financial return series. Furthermore, dynamics in higher moments are captured by allowing for a time-varying shape parameter in this distribution. An adaptive Markov chain Monte Carlo (MCMC) sampling scheme is used for estimation, employing the Metropolis--Hastings (MH) algorithm with a mixture of Gaussian proposal distributions. A simulation study shows accurate estimation and improved inference of parameters in comparison with a single Gaussian proposal MH method. We illustrate the model by applying it to forecast return series from four international stock market indices, as well as two exchange rates, and generating one step-ahead forecasts of VaR and ES. We apply standard and non-standard tests to these forecasts, as well as to those from some competing methods, and find that the proposed model performs favourably compared to many popular competitors; in particular, it is the only conservative model of risk among the models considered in this work over the period studied, which includes the recent financial crisis. However, an AL conditional ditribution may forecast risk too conservatively, and over-estimate the risk levels by a factor of two. In other words, the model implies the necessity for financial institutions to set aside up to twice as much regulatory capital as they need. With fixed total capital, the capital available to invest is reduced, leading to a lowered profit potential. To address this dilemma, this study develops and employs a two-sided Weibull (TW) distribution to capture potential skewness and fat-tailed behaviour in the conditional financial return distribution for the purposes of risk measurement and management, specifically focusing on the forecasting of VaR and conditional VaR measures. Four volatility model specifications, including both symmetric and nonlinear versions, are considered to capture heteroscedasticity. An adaptive Bayesian MCMC scheme is devised for estimation, inference, and forecasting. A range of conditional return distributions (TW, AL, symmetric, and skewed Student t) are combined with the four volatility specifications to forecast risk measures. The study finds that the GARCH-type volatility specification is much less important than that of the conditional distribution and, while the Student t distribution performs particularly well on VaR forecasting, the two-sided Weibull performs at least equally well for VaR, but the most favourably for conditional VaR forecasting, both prior to as well as during and after the recent financial crisis. Nonetheless, the TW distribution can be bimodal, while the conditional distribution of real financial return series are known to be uni-modal. To address this issue, this study develops a partitioned distribution, combining the Weibull tails with a uni-modal AL centre. The proposed distribution is combined with the GJR-GARCH volatility model, to estimate and forecast the VaR and Conditional VaR. The estimation is via an adaptive MCMC sampling scheme and the MH algorithm, with a more general and flexible mixture of Student t proposal distributions. A simulation study demonstrates the estimation is marginally closer to the true values than the mixture of Gaussian proposal distributions. The model is illustrated via application to real financial return series, generating one-day-ahead forecasts and is compared with several competing models. The forecasts are evaluated by formal and non-formal backtesting methods. The model-fitting performances are demonstrated by a range of residual tests. We find the partitioned distribution forecasts financial tail risks slightly less accurately than the TW, but is most favoured by the residual tests.|
|Description:||Doctor of Philosophy(PhD)|
|Rights and Permissions:||The author retains copyright of this thesis.|
|Type of Work:||PhD Doctorate|
|Appears in Collections:||Sydney Digital Theses (Open Access)|
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