Dynamical Volatilities for Yen-Dollar Exchange Rates

Abstract

We study the continuous time random walk theory from financial tick data of the yen-dollar exchange rate transacted at the Japanese financial market. The dynamical behavior of returns and volatilities in this case is particularly treated at the long-time limit. We find that the volatility for prices shows a power-law with anomalous scaling exponent k = 0.96 (one minute) and 0.86 (ten minutes), and that our behavior occurs in the subdiffusive process. Our result presented will be compared with that of recent numerical calculations.