Estimating Value-At-Risk (Var) Using TIVEX-POT Models

Financial institutions hold risks in their investments that can potentially affect their ability to serve 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 time-varying parameter through explanatory variables (TiVEx) - peaks over thresholds model (POT). The time varying parameters are linked to linear predictor variables through link functions. To estimate parameters, maximum likelihood estimation is used with the time-varying parameters being replaced from the likelihood function of the generalized Pareto distribution. The test series used for the paper was the Philippine Peso-US Dollar exchange rate 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 TiVEx-POT models by dropping covariates were 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 VaR modeling since it has consistent green status on the number of exemptions and lower risk capital.