Using Stratified Sampling Methods To Improve Percentile Estimates In The Context of Risk Measurement
Risk measurement is often based on tail percentiles of distributions that are too complex to estimate without resorting to simulation methods. Too often, these simulation methods require enormous computational effort to generate sufficient data points for precise inference about the distribution tails. This paper explores the efficiency benefits that can be derived by applying stratified sampling to these risk-measurement problems. Observations that are close to the percentile of interest are over-sampled and observations that are far away from the percentile of interest are under-sampled. This is shown to dramatically improve the quality of percentile estimates while simultaneously reducing the computational burden. This paper also explores a method of sampling from non-parametric distribution estimates. The ability to generate random draws from such distribution estimates is a key prerequisite for solving the types of simulation problems associated with credit and operational risk measurement.
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