Stochastic autoregressive volatility model for exchange rates

Abstract

A discrete time model for asset price changes is considered. The volatility process underlying these changes is modeled as a first-order Gaussian autoregressive series. Inversion of the marginal characteristic function of the return process simplifies the assessment of the tail behaviour of the probability density function of returns. The Generalized Method of Moments(GMM) is used to calibrate the model and implement an overidentification test. Daily Euro/USD, Pound/USD, AUD/USD, and Yen/USD exchange rates over the period January 1999 to October 2006 are used to illustrate the methods.

Keywords

• Ornstein-Uhlenbeck process
• stochastic volatility
• characteristic function
• fourier transform
• Generalised Method of Moments