An Importance Sampling Algorithm for Estimating Risk Measures

風險測度估計－重點抽樣法

邱于芬(Yu-fen Chiu)

Risk Measure ； Monte Carlo Simulation ； Important Sampling ； 風險測度 ； 蒙地卡羅模擬 ； 重點抽樣

風險管理學報

19卷1期（2017 / 06 / 01）

43 - 51

英文

We propose a simple importance sampling algorithm for estimating tail probabilities of sums of positively correlated lognormals driven by a correlated Gaussian vector X. This algorithm can be applied to estimating risk measures of portfolio of risky assets. Also, the algorithm can be used for computing the values of basket options or Asian options. The algorithm is based on a special decomposition of the correlated Gaussian vector X. The decomposition utilizing the spectral decomposition of the covariance matrix of X. The algorithm is guaranteed to produce variance reduction over crude Monte Carlo approach. Numerical examples show that the estimator has constant coefficient of variation. This suggests the proposed estimator has bounded relative error.

本研究提出一種簡單的重點抽樣演算法，用於估計由正相關高斯向量X所驅動的對數常態變數之和的尾部機率。該演算法除了可用於估計風險性資產組 合的風險測度之外，亦可應用於一籃子選擇權或亞式選擇權的評價。該演算法利用X的共變矩陣的光譜分解進行變數分解，所產生的估計保證比傳統蒙特卡羅法產生的估計有較低的變異數。數值結果顯示，本演算法的估計具有不變的變異係數，這說明本文所提出的估計方法具備有限之相對誤差。

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