Conditional Monte Carlo Estimation of Quantile Sensitivities

• 成果类型: Article
• 署名作者: Fu, Michael C.; Hong, L. Jeff; Hu, Jian-Qiang
• 署名单位: University System of Maryland; University of Maryland College Park; University System of Maryland; University of Maryland College Park; Hong Kong University of Science & Technology; Fudan University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.1090.1090
• 发表日期: 2009
• 页码: 2019-2027
• 关键词: Quantiles; Value at risk; Credit risk; Monte Carlo simulation; gradient estimation

摘要

Estimating quantile sensitivities is important in many optimization applications, from hedging in financial engineering to service-level constraints in inventory control to more general chance constraints in stochastic programming. Recently, Hong (Hong, L. J. 2009. Estimating quantile sensitivities. Oper. Res. 57 118-130) derived a batched infinitesimal perturbation analysis estimator for quantile sensitivities, and Liu and Hong (Liu, G., L. J. Hong. 2009. Kernel estimation of quantile sensitivities. Naval Res. Logist. 56 511-525) derived a kernel estimator. Both of these estimators are consistent with convergence rates bounded by n(-1/3) and n(-2/5), respectively. In this paper, we use conditional Monte Carlo to derive a consistent quantile sensitivity estimator that improves upon these convergence rates and requires no batching or binning. We illustrate the new estimator using a simple but realistic portfolio credit risk example, for which the previous work is inapplicable.