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 2004
• Subjects: Finance and Financial Management; Portfolio and Security Analysis
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/2630; https://doi.org/10.1088/1469-7688/4/2/002
• Institution: Singapore Management University

This paper studies the modelling of large diversified portfolios in a financial market with jump-diffusion 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 sufficiently large. Analytical and Monte Carlo value-at-risk can be computed for the portfolios based on their asymptotic dynamics.