The Value-at-Risk Estimation For Currency Markets Based On Fractal Theory

Exchange rate as an important part in the economic and trade, in today's economic and trade globalization environment, plays a more and more important role. Since the collapse of the bretton woods system since the 1970 s, more and more countries began to implement the floating exchange rate system. But compared with the fixed exchange rate, floating exchange rate system is not the same as completely free floating exchange rate. It is based on a certain management system under the floating, therefore also contributed to the international financial market fluctuations. The fluctuations bring to the economic and trade activities must have the risk of uncertainty, inevitably produce risk. In recent decades of international economic and trade activities, the exchange rate risk has a certain impact on the economic and trade activities and harm. But in recent years, the global economy are also suffering from the most severe test since the 1970 s. In October 2009, the euro crisis broke out. International main complex volatility in exchange rates, currency market risk increases.In this paper, we use multifractal theory to analyze the fractal character of foreign exchange market. Then the ARFIMA-FIGARCH model is utilized for the long-memory and VaR measurement.The paper first introduces the research status of the VaR measurement for foreign exchange market. Then based on the Fractal Market Hypothesis, the writer proposes that utilizing the multifractal theory to analyze the fractal character of foreign exchange market from the microcosmic view. Next, based on the predecessors' researches, we apply the ARFIMA-FIGARCH model to the foreign exchange market for the long-memory as well as VaR measurement.The achievements of the paper consist three portions. The first section is for the foreign exchange market research in the microcosmic view with the multifractal theory; the second is for employing ARFIMA-FIGARCH model for the long-memory of return process and fluctuation process of foreign exchange market; then based on the VaR theory, we combine the FIGARCH model which contains the fractal difference process and VaR estimation process for the five currency markets; the third is that the work of this paper is novel, and it adds the empirical study literature to the foreign exchange market.