Asymptotic Dynamics and Value-at-Risk of Large Diversified Portfolios in a Jump-Diffusion Market - Lim, Kian Guan (Institutional Knowledge at Singapore Management University, 2003)
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.