Abstract:
The main purpose of this study was to model Conditional Value-at-Risk using
Tukey’s g-and-h distribution and employ the maximum approximated likelihood
method for parameter estimation, subsequently contrasting Tukey’s distribution
with Cornish-Fisher and classical approaches. While the Cornish-Fisher method
modifies the normal quantile to account for skewness and kurtosis, the classical
methodology assumes that asset returns follow a normal distribution. Historical
daily return data from January 1, 2003, to January 17, 2011, from Spain were
used in the study. Conditional Value-at-Risk (CVaR), also known as Expected
Shortfall (ES), is a risk indicator that shows the expected loss at a given confidence
level when a loss exceeds the Value-at-Risk. The maximum approximated
likelihood estimator is one approach used to estimate the parameters of Tukey’s
distribution. Because of its light-tailed assumption, the classical technique results
in the least extreme losses. Due to its sensitivity to skewness and kurtosis
modifications, the Cornish-Fisher approach produces noticeably larger tail losses;
however, at very high confidence levels, this may introduce instability. Without
the dramatic divergence observed in the Cornish-Fisher method, the MALE-based
Tukey’s model captures heavy-tailed traits with smoother and more stable tail behavior.
These findings imply that MALE provides a more reliable paradigm for
measuring high risk. These findings have applications in stress testing, regulatory
calculation, and risk management, where precise extreme tail risk estimation is
essential. Model errors, parameter uncertainty, data selection, and inadequate
data may still impact the proposed strategy. Consequently, even while MALE
enhances tail risk prediction, its efficacy depends on adequate data and trustworthy
estimation techniques. As a recommendation, to further confirm the MALE
model’s resilience in measuring severe risk, additional research should examine its
performance in various market scenarios and on larger datasets.
