Estimating and forecasting portfolio’s Value-at-Risk with wavelet-based extreme value theory: Evidence from crude oil prices and US exchange rates

Abstract

This article proposes a wavelet-based extreme value theory (W-EVT) approach to estimate and forecast portfolio’s Value-at-Risk (VaR) given the stylized facts and complex structure of financial data. Our empirical application to portfolios of crude oil prices and US dollar exchange rates shows that the W-EVT models provide an effective and powerful tool for gauging extreme moments and improving the accuracy of portfolio’s VaR estimates and forecasts after noise is removed from the original data.

Keywords:

• stochastic processes
• wavelet analysis
• extreme value theory
• VaR
• oil-exchange rate portfolios

JEL Classification:

• C52
• C53
• G17

The online version of this article is available Open Access

The online version of this article is available Open Access

Notes

1 In a related study, Reboredo and Rivera-Castro (2013) use a DWT approach to examine the relationship between oil prices and US dollar exchange rates over different time scales. They find evidence of no dependence between the variables of interest in the pre-crisis period, but evidence of contagion and negative dependence after the onset of the crisis. Our study thus differs from Reboredo and Rivera-Castro (2013) in that we focus on the underlying relationships between oil prices and exchange rates in the presence of extreme values and after noise removal.

2 The “optimum” value of the threshold level, is calculated according to Donoho (1995) as λ =  where T is the length of the decomposed vector, and σ² the variance of the noise, which is estimated from the variance of the detailed coefficients at the first decomposition level.

3 The results regarding the descriptive statistics can be made available on request.

4 The parameter estimates of the three tests were obtained via the maximum-likelihood method. The acceptance and rejection of the p value were compared to the critical values at 10, 5 and 1 % levels. All the test estimates were obtained by easy-fit software.

5 The portfolio’s return is computed according to Eq. (1212 ). The results of the distribution choice for portfolios are available on request.