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

Dennis Mapa (), Peter Julian Cayton and Mary Therese Lising

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Value-at-Risk; Extreme Value Theory; Generalized Pareto Distribution; Time-Varying Parameters; Use of Explanatory Variables; GARCH modeling; Peaks-over-Thresholds Model (search for similar items in EconPapers)
JEL-codes: C01 C22 C53 G12 (search for similar items in EconPapers)
Date: 2009-12
New Economics Papers: this item is included in nep-ban, nep-ecm and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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