Estimating Value-at-Risk (VaR) using TiVEx-POT Models

Mapa, Dennis S. and Cayton, Peter Julian and Lising, Mary Therese (2009): Estimating Value-at-Risk (VaR) using TiVEx-POT Models.

Abstract

Financial institutions hold risks in their investments that can potentially affect their ability to serve their clients. For banks to weigh their risks, Value-at-Risk (VaR) methodology is used, which involves studying the distribution of losses and formulating a statistic from this distribution. From the myriad of models, this paper proposes a method of formulating VaR using the Generalized Pareto distribution (GPD) with time-varying parameter through explanatory variables (TiVEx) - peaks over thresholds model (POT). The time varying parameters are linked to the linear predictor variables through link functions. To estimate parameters of the linear predictors, maximum likelihood estimation is used with the time-varying parameters being replaced from the likelihood function of the GPD. The test series used for the paper was the Philippine Peso-US Dollar exchange rate with horizon from January 2, 1997 to March 13, 2009. Explanatory variables used were GARCH volatilities, quarter dummies, number of holiday-weekends passed, and annual trend. Three selected permutations of modeling through TiVEx-POT by dropping other covariates were also conducted. Results show that econometric models and static POT models were better-performing in predicting losses from exchange rate risk, but simple TiVEx models have potential as part of the VaR modelling philosophy since it has consistent green status on the number exemptions and lower quadratic loss values.

• Item Type: MPRA Paper
• Language: English
• Keywords: Value-at-Risk, Extreme Value Theory, Generalized Pareto Distribution, Time-Varying Parameters, Use of Explanatory Variables, GARCH modeling, Peaks-over-Thresholds Model
• Subjects: G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics

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