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

Yu Ge, Guangwu Liu and Houcai Shen ()
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Yu Ge: School of Management and Engineering, Nanjing University, Nanjing 210093, P. R. China2Department of Management Sciences, College of Business, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, P. R. China
Guangwu Liu: Department of Management Sciences, College of Business, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, P. R. China
Houcai Shen: School of Management and Engineering, Nanjing University, Nanjing 210093, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2024, vol. 41, issue 05, 1-19

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 Γ−1, much faster than the rate of the CVaR estimator in the continuous case which is Γ−2/3, where Γ denotes the sampling budget required by the nested simulation procedure. Performance of the proposed estimator is demonstrated using numerical examples.

Keywords: Nested simulation; conditional Value-at-Risk; Monte Carlo simulation; statistical analysis (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0217595923500379

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