A Large Deviations Analysis of Quantile Estimation with Application to Value at Risk

Loading...
Thumbnail Image

Files

Nicholson.pdf (355.87 KB)
No. of downloads: 1487

Publication or External Link

Date

2005-07-01T12:31:49Z

Advisor

Citation

DRUM DOI

Abstract

Quantile estimation has become increasingly important, particularly in the financial industry, where Value-at-Risk has emerged as a standard measurement tool for controlling portfolio risk. In this paper we apply the theory of large deviations to analyze various simulation-based quantile estimators. First, we show that the coverage probability of the standard quantile estimator converges to one exponentially fast with sample size. Then we introduce a new quantile estimator that has a provably faster convergence rate. Furthermore, we show that the coverage probability for this new estimator can be guaranteed to be 100% with sufficiently large, but finite, sample size. Numerical experiments on a VaR example illustrate the potential for dramatic variance reduction.

Notes

Rights