An Econometric Analysis of Drawdown Based Measures

In this chapter, we discuss two risk measures based on drawdown process and closely related to market crises: the drawdown of a fixed level and the speed of market crash. They allow us to study the first time that the asset’s price deviates from its current maximum by a certain threshold value and the velocity at which this drop occurs, respectively. Consequently, the former, is a relative measure of the losses linked to an asset, while the latter, quantifies the speed at which these losses occur. In order to study these risk measures, we consider tick-by-tick prices of two assets, listed on the Italian Stock Exchange. We implement an empirical investigation involving estimation and simulation of widely used econometric models such as Autoregressive Moving Average (ARMA) models, Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models and Exponential GARCH (EGARCH) models. We test the ability of each model to reproduce the volatility autocorrelation, a typical feature of financial time series, and then we analyze their capacity to reproduce the drawdown of fixed level and the speed of market crash, compared to real data.