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Optimal portfolios when volatility can jump

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  • Branger, Nicole
  • Schlag, Christian
  • Schneider, Eva
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    Abstract

    We consider an asset allocation problem in a continuous-time model with stochastic volatility and jumps in both the asset price and its volatility. First, we derive the optimal portfolio for an investor with constant relative risk aversion. The demand for jump risk includes a hedging component, which is not present in models without volatility jumps. We further show that the introduction of derivative contracts can have substantial economic value. We also analyze the distribution of terminal wealth for an investor who uses the wrong model, either by ignoring volatility jumps or by falsely including such jumps, or who is subject to estimation risk. Whenever a model different from the true one is used, the terminal wealth distribution exhibits fatter tails and (in some cases) significant default risk.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Banking & Finance.

    Volume (Year): 32 (2008)
    Issue (Month): 6 (June)
    Pages: 1087-1097

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    Handle: RePEc:eee:jbfina:v:32:y:2008:i:6:p:1087-1097

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    Web page: http://www.elsevier.com/locate/jbf

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    References

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    1. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    2. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
    3. Bhamra, Harjoat S. & Uppal, Raman, 2006. "The role of risk aversion and intertemporal substitution in dynamic consumption-portfolio choice with recursive utility," Journal of Economic Dynamics and Control, Elsevier, vol. 30(6), pages 967-991, June.
    4. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
    5. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-61.
    6. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
    7. Liu, Jun & Pan, Jun, 2003. "Dynamic Derivative Strategies," Working papers 4334-02, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    8. 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, 02.
    9. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    10. Dieckmann, Stephan & Gallmeyer, Michael, 2005. "The equilibrium allocation of diffusive and jump risks with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 29(9), pages 1547-1576, September.
    11. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, 06.
    12. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management.
    13. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06.
    14. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
    15. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
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    Cited by:
    1. Branger, Nicole & Kraft, Holger & Meinerding, Christoph, 2014. "Partial information about contagion risk, self-exciting processes and portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 18-36.
    2. Chung, Kee H. & Smith, William T. & Wu, Tao L., 2009. "Time diversification: Definitions and some closed-form solutions," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1101-1111, June.
    3. Muck, Matthias, 2010. "Trading strategies with partial access to the derivatives market," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1288-1298, June.
    4. Zieling, Daniel & Mahayni, Antje & Balder, Sven, 2014. "Performance evaluation of optimized portfolio insurance strategies," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 212-225.
    5. Weinbaum, David, 2010. "Preference heterogeneity and asset prices: An exact solution," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2238-2246, September.
    6. Branger, Nicole & Larsen, Linda Sandris, 2013. "Robust portfolio choice with uncertainty about jump and diffusion risk," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5036-5047.
    7. Gao, Jianwei, 2010. "An extended CEV model and the Legendre transform-dual-asymptotic solutions for annuity contracts," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 511-530, June.
    8. Branger, Nicole & Hansis, Alexandra, 2012. "Asset allocation: How much does model choice matter?," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1865-1882.
    9. Konermann, Patrick & Meinerding, Christoph & Sedova, Olga, 2013. "Asset allocation in markets with contagion: The interplay between volatilities, jump intensities, and correlations," Review of Financial Economics, Elsevier, vol. 22(1), pages 36-46.

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