Hybrid dynamics for currency modeling

Abstract

We present a simple hybrid dynamical model as a tool to investigate behavioral strategies based on trend following. The multiplicative symbolic dynamics are generated using a lognormal diffusion model for the at-the-money implied volatility term structure. Thus, are model exploits information from derivative markets to obtain qualititative properties of the return distribution for the underlier. We apply our model to the JPY-USD exchange rate and the corresponding 1mo., 3mo., 6mo. and 1yr. implied volatilities. Our results indicate that the modulation of autoregressive trend following using derivative-based signals significantly improves the fit to the distribution of times between successive sign flips in the underlier time series.