Nested Simulation for Conditional Value-at-Risk with Discrete Losses

Author:

Ge Yu12ORCID,Liu Guangwu2ORCID,Shen Houcai1ORCID

Affiliation:

1. School of Management and Engineering, Nanjing University, Nanjing 210093, P. R. China

2. Department of Management Sciences, College of Business, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, P. R. China

Abstract

Nested simulation has been an active area of research in recent years, with an important application in portfolio risk measurement. While majority of the literature has been focusing on the continuous case where portfolio loss is assumed to follow a continuous distribution, monetary losses of a portfolio in practice are usually measured in discrete units, oftentimes due to the practical consideration of meaningful decimal places for a given level of precision in risk measurement. In this paper, we study a nested simulation procedure for estimating conditional Value-at-Risk (CVaR), a popular risk measure, in the case where monetary losses of the portfolio take discrete values. Tailored to the discrete nature of portfolio losses, we propose a rounded estimator and show that when the portfolio loss follows a sub-Gaussian distribution or has a sufficiently high-order moment, the mean squared error (MSE) of the resulting CVaR estimator decays to zero at a rate close to [Formula: see text], much faster than the rate of the CVaR estimator in the continuous case which is [Formula: see text], where [Formula: see text] denotes the sampling budget required by the nested simulation procedure. Performance of the proposed estimator is demonstrated using numerical examples.

Funder

National Natural Science Foundation of China

Research Grants Council (RGC) of Hong Kong under the General Research Fund Project

NSFC/RGC Joint Research Scheme

Publisher

World Scientific Pub Co Pte Ltd

Subject

Management Science and Operations Research,Management Science and Operations Research

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