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Portfolio Choice in Markets with Contagion

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  • Yacine Aït-Sahalia
  • Thomas Robert Hurd

Abstract

We consider the problem of optimal investment and consumption in a class of multidimensional jump-diffusion models in which asset prices are subject to mutually exciting jump processes. This captures a type of contagion where each downward jump in an asset's price results in increased likelihood of further jumps, both in that asset and in the other assets. We solve in closed-form the dynamic consumption-investment problem of a log-utility investor in such a contagion model, prove its optimality and discuss features of the solution, including flight-to-quality. The clustering of jumps gives rise to a time-varying optimal asset allocation: as jumps predict more jumps, the portfolio should be optimally rebalanced to hedge the risk of future jumps. The exponential and power utility investors are also considered: in these cases, the optimal strategy can be characterized as a distortion of the strategy of a corresponding non-contagion investor.

Suggested Citation

  • Yacine Aït-Sahalia & Thomas Robert Hurd, 2016. "Portfolio Choice in Markets with Contagion," Journal of Financial Econometrics, Oxford University Press, vol. 14(1), pages 1-28.
    • Handle: RePEc:oup:jfinec:v:14:y:2016:i:1:p:1-28.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbv024
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    Cited by:

    1. Lee, Yongwoong & Yang, Kisung, 2019. "Modeling diversification and spillovers of loan portfolios' losses by LHP approximation and copula," International Review of Financial Analysis, Elsevier, vol. 66(C).
    2. Kraft, Holger & Weiss, Farina, 2023. "Pandemic portfolio choice," European Journal of Operational Research, Elsevier, vol. 305(1), pages 451-462.
    3. Lijun Bo & Agostino Capponi & Claudia Ceci, 2017. "Risk-Minimizing Hedging of Counterparty Risk," Papers 1709.01115, arXiv.org.
    4. Aït-Sahalia, Yacine & Matthys, Felix, 2019. "Robust consumption and portfolio policies when asset prices can jump," Journal of Economic Theory, Elsevier, vol. 179(C), pages 1-56.
    5. Le Courtois, Olivier & Menoncin, Francesco, 2015. "Portfolio optimisation with jumps: Illustration with a pension accumulation scheme," Journal of Banking & Finance, Elsevier, vol. 60(C), pages 127-137.
    6. Warshaw, Evan, 2019. "Extreme dependence and risk spillovers across north american equity markets," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 237-251.
    7. Cheng, Chunli & Hilpert, Christian & Miri Lavasani, Aidin & Schaefer, Mick, 2023. "Surrender contagion in life insurance," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1465-1479.
    8. Yang Shen & Bin Zou, 2021. "Mean-Variance Portfolio Selection in Contagious Markets," Papers 2110.09417, arXiv.org.
    9. Yaacov Kopeliovich & Michael Pokojovy & Julia Bernatska, 2024. "On Merton's Optimal Portfolio Problem with Sporadic Bankruptcy for Isoelastic Utility," Papers 2403.15923, arXiv.org, revised Nov 2024.
    10. Dassios, Angelos & Zhao, Hongbiao, 2013. "Exact simulation of Hawkes process with exponentially decaying intensity," LSE Research Online Documents on Economics 51370, London School of Economics and Political Science, LSE Library.
    11. Yuki Toyoshima & Shigeyuki Hamori, 2018. "Measuring the Time-Frequency Dynamics of Return and Volatility Connectedness in Global Crude Oil Markets," Energies, MDPI, vol. 11(11), pages 1-18, October.
    12. Tiwari, Aviral Kumar & Cunado, Juncal & Gupta, Rangan & Wohar, Mark E., 2018. "Volatility spillovers across global asset classes: Evidence from time and frequency domains," The Quarterly Review of Economics and Finance, Elsevier, vol. 70(C), pages 194-202.
    13. Ji, Qiang & Liu, Bing-Yue & Cunado, Juncal & Gupta, Rangan, 2020. "Risk spillover between the US and the remaining G7 stock markets using time-varying copulas with Markov switching: Evidence from over a century of data," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).
    14. Bo, Lijun & Tang, Dan & Wang, Yongjin, 2017. "Optimal investment of variance-swaps in jump-diffusion market with regime-switching," Journal of Economic Dynamics and Control, Elsevier, vol. 83(C), pages 175-197.
    15. Qu, Yan & Dassios, Angelos & Zhao, Hongbiao, 2023. "Shot-noise cojumps: exact simulation and option pricing," LSE Research Online Documents on Economics 111537, London School of Economics and Political Science, LSE Library.
    16. Feng Shi & John Paul Broussard & G. Geoffrey Booth, 2025. "The complex nature of financial market microstructure: the case of a stock market crash," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 20(1), pages 1-40, January.
    17. Bernd Scherer, 2020. "Alternative risk premia: contagion and portfolio choice," Journal of Asset Management, Palgrave Macmillan, vol. 21(3), pages 178-191, May.
    18. Robert Jarrow, 2018. "An Equilibrium Capital Asset Pricing Model in Markets with Price Jumps and Price Bubbles," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 1-33, June.
    19. Grabowski, Wojciech & Welfe, Aleksander, 2020. "The Tobit cointegrated vector autoregressive model: An application to the currency market," Economic Modelling, Elsevier, vol. 89(C), pages 88-100.
    20. Aleksy Leeuwenkamp & Wentao Hu, 2023. "New general dependence measures: construction, estimation and application to high-frequency stock returns," Papers 2309.00025, arXiv.org.
    21. Buccioli, Alice & Kokholm, Thomas & Nicolosi, Marco, 2019. "Expected shortfall and portfolio management in contagious markets," Journal of Banking & Finance, Elsevier, vol. 102(C), pages 100-115.

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