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Asymptotic dynamics and value-at-risk of large diversified portfolios in a jump-diffusion market

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  • Lim Kian Guan
  • Liu Xiaoqing
  • Tsui Kai Chong

Abstract

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.

Suggested Citation

  • Lim Kian Guan & Liu Xiaoqing & Tsui Kai Chong, 2004. "Asymptotic dynamics and value-at-risk of large diversified portfolios in a jump-diffusion market," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 129-139.
    • Handle: RePEc:taf:quantf:v:4:y:2004:i:2:p:129-139
    DOI: 10.1080/14697680400000017
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    References listed on IDEAS

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    1. Jun Pan & Darrell Duffie, 2001. "Analytical value-at-risk with jumps and credit risk," Finance and Stochastics, Springer, vol. 5(2), pages 155-180.
    2. Norbert Hofmann & Eckhard Platen, 2000. "Approximating Large Diversified Portfolios," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 77-88, January.
    3. Tomas Björk & Bertil Näslund, 1998. "Diversified Portfolios in Continuous Time," Review of Finance, European Finance Association, vol. 1(3), pages 361-387.
    4. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    5. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
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    Cited by:

    1. Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 184, Quantitative Finance Research Centre, University of Technology, Sydney.

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