A survey of risk and ambiguity: an application to the GARCH(1,1) model with exchange rate data.

Abstract

The assumption of normality in many risk management models is not always representative of the sample distribution at hand. Applying a uniform approach to a non-uniform population can produce biased and unreliable estimators that can have adverse effects to the consequences of decision-making. Since advancements in both research and statistical tools enable models to be more flexible than before, the purpose of this text is to examine to what extend this can be verified using exchange rate data, which is often characterized by the pronounced leptokurtosis and volatility that is found in such time series. Two GARCH(1,1) models are constructed for each of the three exchange rates in the study; one using the normal distribution, and the other using Student’s t distribution. The proxy for differences in the dynamics as implied by both approaches is translated in the parameter for persistence. Results support that a distribution with more mass in the tails is superior to the normal distribution for the three exchange rate returns in the study, as defined by information criteria. Also, the persistent parameter is different in all accounts between the two distribution approaches: the estimated persistence using Student’s t distribution is higher for USD/NOK and USD/YEN, but lower for USD/EUR, compared to estimates using the normal distribution. While these findings cannot be generalized asymptotically, they illustrate the deviation in parameter estimation due to different methodological assumptions, and promote a multidisciplinary approach to problem solving.