On Value at Risk for foreign exchange rates - the copula approach

TL;DR

This paper proposes a copula-based method to estimate the Value at Risk for portfolios of foreign exchange currencies, focusing on power-law tail behaviors in returns, demonstrated with EUR and CHF in Poland.

Contribution

It introduces a novel copula approach assuming power-law tails for FX returns, enhancing VaR estimation accuracy for emerging markets.

Findings

Power-law tail behavior observed in FX returns.

Copula approach effectively models joint tail risks.

Practical application to EUR and CHF exchange rates.

Abstract

The aim of this paper is to determine the Value at Risk (VaR) of the portfolio consisting of long positions in foreign currencies on an emerging market. Basing on empirical data we restrict ourselves to the case when the tail parts of distributions of logarithmic returns of these assets follow the power laws and the lower tail of associated copula C follows the power law of degree 1. We will illustrate the practical usefulness of this approach by the analysis of the exchange rates of EUR and CHF at the Polish forex market.