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.