Dynamical Volatilities for Yen-Dollar Exchange Rates

TL;DR

This paper analyzes the long-term behavior of yen-dollar exchange rate returns and volatilities using continuous time random walk theory, revealing subdiffusive power-law scaling in financial data.

Contribution

It applies continuous time random walk theory to financial tick data, uncovering subdiffusive power-law scaling of volatility at long times, which is a novel insight.

Findings

Volatility exhibits power-law scaling with exponents 0.96 (1 min) and 0.86 (10 min).

The process is characterized as subdiffusive.

Results are compared with recent numerical simulations.

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.