Asymptotic Dynamics and Value-at-Risk of Large Diversified Portfolios in a Jump-Diffusion Market

• Main Authors: Lim, Kian Guan, Liu, Xiaoqing, Tsui, Kai Chong
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2003
• Subjects: Corporate Finance; Finance and Financial Management; Portfolio and Security Analysis
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/1910; https://ink.library.smu.edu.sg/context/lkcsb_research/article/2909/viewcontent/0703paper.pdf
• Institution: Singapore Management University

This paper studies the modelling of large diversi ed portfolios in a nancial market with jump-di usion risks. The portfolios considered include three categories: equal money-weighted portfolios, risk minimizing portfolios, and market indices. Reduced-form dynamics driven jointly by one Brownian Motion and one Poisson process are derived for the asymptotics of such portfolios. We prove that derivatives written on a portfolio can be priced by treating the asymptotic dynamics as the underlying process if the number of assets in the portfolio is su ciently large. Analytical and Monte Carlo Value-at-Risk (VaR) can be computed for the portfolios based on their asymptotic dynamics.