Extreme quantile estimation based on financial time series

ABSTRACT

Estimation of market risk is an important problem in finance. Two well-known risk measures, viz., value at risk and median shortfall, turn out to be extreme quantiles of the marginal distribution of asset return. Time series on asset returns are known to exhibit certain stylized facts, such as heavy tails, skewness, volatility clustering, etc. Therefore, estimation of extreme quantiles in the presence of such features in the data seems to be of natural interest. It is difficult to capture most of these stylized facts using one specific time series model. This motivates nonparametric and extreme value theory-based estimation of extreme quantiles that do not require exact specification of the asset return model. We review these quantile estimators and compare their known properties. Their finite sample performance are compared using Monte Carlo simulation. We propose a new estimator that exhibits encouraging finite sample performance while estimating extreme quantile in the right tail region.

KEYWORDS:

• Median shortfall
• Quantile estimation
• VaR

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G05
• 60F05
• 91G70
• 91G10

Acknowledgments

The authors are thankful to the esteemed reviewer for a positive and encouraging report, and also for pointing out some corrections that lead to improvement of the manuscript.

Funding

This research was supported by UGC Rajiv Gandhi National Fellowship of the second author.