Journal of Risk Model Validation

Risk.net

Value-at-risk estimation with the Carr–Geman–Madan–Yor process: an empirical study on foreign exchange rates

Sun-Yong Choi

  • We investigate the performance of the CGMY process to find whether the CGMY distribution is appropriate for describing the fat tails of the distribution of FX rate return.
  • We compare four other VaR models and their methodologies are then applied to three major foreign exchange rates: EUR/JPY, EUR/USD, and USD/JPY.
  • We propose a new procedure to find the best size of estimation window for the VaR model, using which we choose the best size for each VaR model and compare the respective VaR estimates.

ABSTRACT

To discover whether the Carr-Geman-Madan-Yor (CGMY) distribution, a Lévy process that can have an infinite number of jumps in a finite time interval, is appropriate for describing the fat tails of the distribution of foreign exchange (FX) rate returns, we investigate its performance in estimating the risk of FX rates. We estimate valu-at-risk (VaR), one of the most popular concepts in the area of risk management, for FX rate returns. To enhance the robustness of the estimation results, we use other VaR models, such as historical simulation, the generalized autoregressive conditional heteroscedasticity (GARCH) model and conditional extreme value theory (EVT). Our four methodologies are applied to three major foreign exchange rates (EUR/JPY, EUR/USD and USD/JPY) by using a different size estimation windows for each model to forecast one-day-ahead VaR. We propose a new procedure to find the best size of estimation window for each VaR model, with which we compare the respective VaR estimates. The conditional EVT and CGMY distributions provide superior forecasting performance for all three rates's daily returns, respectively. Furthermore, the performance of the other methods can be significantly improved by adjusting the size of the estimation window.

To continue reading...

You need to sign in to use this feature. If you don’t have a Risk.net account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here: