Modeling drawdowns and drawups in financial markets - Risk.net

64
Beatriz Vaz de Melo Mendes and Vinicius Ratton Brandi
FIGURE 4 QQ-plots of the fitted MGPD (upper row) and the stretched exponential
(lower row) of the drawdowns (left) and drawups (right) in the case of the Hang
Seng index.
MGPD fit
Stretched exponential fit
MGPD fit
Drawdowns Drawups
Stretched exponential fit
Drawdowns Drawups
observe the masking effect. The largest observation had, under the stretched
exponential, an almost perfect fit, at the cost of a poor fit for drawups between
13% and 24%. The MGPD fitted the whole data set well, spotting a moderate
(24.9%) and an extreme outlier (26%).
In summary, for many data sets the stretched exponential provided a poor fit
for a few extreme observations. According to Johansen and Sornette (2001), these
atypical observations could belong to a different regime and might be considered
outliers. However, for most of these data sets the MGPD was able to provide a
good fit for most of the extreme points as well as the bulk of the data. Despite its
improvement, there is still a small percentage of points with poor adherence to
the MGPD. We wonder if such points could be an effect of long-lasting sequences
of drops (rises), or an effect of spurious correlation. Under either assumption they
could be considered outliers.
To complete our analysis, Figure 6 illustrates the different perception of risk
provided by the drawdowns. This figure shows in the x-axis the exceedance probabilities
(0.002, 0.004, 0.006, 0.008, 0.010, 0.020, 0.030, 0.040) of observing
URL: www.thejournalofrisk.com Journal of Risk