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When do jumps matter for portfolio optimization?

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  • Ascheberg, Marius
  • Branger, Nicole
  • Kraft, Holger

Abstract

We consider the continuous-time portfolio optimization problem of an investor with constant relative risk aversion who maximizes expected utility of terminal wealth. The risky asset follows a jump-diffusion model with a diffusion state variable. We propose an approximation method that replaces the jumps by a diffusion and solve the resulting problem analytically. Furthermore, we provide explicit bounds on the true optimal strategy and the relative wealth equivalent loss that do not rely on results from the true model. We apply our method to a calibrated affine model and find that relative wealth equivalent losses are below 1.16% if the jump size is stochastic and below 1% if the jump size is constant and ... 5. We perform robustness checks for various levels of risk-aversion, expected jump size, and jump intensity.

Suggested Citation

  • Ascheberg, Marius & Branger, Nicole & Kraft, Holger, 2013. "When do jumps matter for portfolio optimization?," SAFE Working Paper Series 16, Leibniz Institute for Financial Research SAFE.
    • Handle: RePEc:zbw:safewp:16
    DOI: 10.2139/ssrn.2259630
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    References listed on IDEAS

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    1. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    2. Larsen, Linda Sandris & Munk, Claus, 2012. "The costs of suboptimal dynamic asset allocation: General results and applications to interest rate risk, stock volatility risk, and growth/value tilts," Journal of Economic Dynamics and Control, Elsevier, vol. 36(2), pages 266-293.
    3. Jun Liu & Francis A. Longstaff & Jun Pan, 2003. "Dynamic Asset Allocation with Event Risk," Journal of Finance, American Finance Association, vol. 58(1), pages 231-259, February.
    4. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    5. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    7. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
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    Cited by:

    1. Amaro de Matos, João & Silva, Nuno, 2014. "Consuming durable goods when stock markets jump: A strategic asset allocation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 86-104.

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    More about this item

    Keywords

    Optimal investment; jumps; stochastic volatility; welfare loss;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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