Physical Sciences and Mathematics Commons^™

Variance Reduction Techniques For Estimating Quantiles And Value-At-Risk, Fang Chu

Dissertations

Quantiles, as a performance measure, arise in many practical contexts. In finance, quantiles are called values-at-risk (VARs), and they are widely used in the financial industry to measure portfolio risk. When the cumulative distribution function is unknown, the quantile can not be computed exactly and must be estimated. In addition to computing a point estimate for the quantile, it is important to also provide a confidence interval for the quantile as a way of indicating the error in the estimate. A problem with crude Monte Carlo is that the resulting confidence interval may be large, which is often the case …