Implications of Nonlinear Dynamics for Financial Risk Management

Abstract

This paper demonstrates that when log price changes are not IID, their conditional density may be more accurate than their unconditional density for describing short-term behavior. Using the BDS test of independence and identical distribution, daily log price changes in four currency futures contracts are found to be not IID. While there appear to be no predictable conditional mean changes, conditional variances are predictable, and can be described by an autoregressive volatility model that seems to capture all the departures from independence and identical distribution. Based on this model, daily log price changes are decomposed into a predictable part, which is described parametrically by the autoregressive volatility model, and an unpredictable part, which can be modeled by an empirical density, either parametrically or nonparametrically. This two-step seminonparametric method yields a conditional density for daily log price changes, which has a number of uses in financial risk management.