IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v252y2016i2p676-686.html
   My bibliography  Save this article

Numerical approximations of optimal portfolios in mispriced asymmetric Lévy markets

Author

Listed:
  • Buckley, Winston
  • Long, Hongwei
  • Marshall, Mario

Abstract

We present numerical approximations of optimal portfolios in mispriced Lévy markets under asymmetric information for informed and uninformed investors having logarithmic preference. We apply our numerical scheme to Kou (2002) jump-diffusion markets by deriving analytic formulas for the first two derivatives of the underlying portfolio objective function which depend only on the Lévy measure of the jump-generating process. Optimal portfolios are then simulated using the Box–Muller algorithm, Newton’s method and incomplete Beta functions. Convergence dynamics and trajectories of sample paths of optimal portfolios for both investors are presented at different levels of information asymmetry, mispricing, horizon, asymmetry in the Kou density, jump intensity, volatility, mean-reversion speed, and Sharpe ratios. We also apply the proposed Newton’s algorithm to compute optimal portfolios for investors in Variance Gamma markets via instantaneous centralized moments of returns.

Suggested Citation

  • Buckley, Winston & Long, Hongwei & Marshall, Mario, 2016. "Numerical approximations of optimal portfolios in mispriced asymmetric Lévy markets," European Journal of Operational Research, Elsevier, vol. 252(2), pages 676-686.
  • Handle: RePEc:eee:ejores:v:252:y:2016:i:2:p:676-686
    DOI: 10.1016/j.ejor.2016.01.050
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221716000965
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Fu, Chenpeng & Lari-Lavassani, Ali & Li, Xun, 2010. "Dynamic mean-variance portfolio selection with borrowing constraint," European Journal of Operational Research, Elsevier, vol. 200(1), pages 312-319, January.
    3. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    4. Buckley, Winston S. & Brown, Garfield O. & Marshall, Mario, 2012. "A mispricing model of stocks under asymmetric information," European Journal of Operational Research, Elsevier, vol. 221(3), pages 584-592.
    5. Ning Cai & S. G. Kou, 2011. "Option Pricing Under a Mixed-Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 57(11), pages 2067-2081, November.
    6. Buckley, Winston & Long, Hongwei & Perera, Sandun, 2014. "A jump model for fads in asset prices under asymmetric information," European Journal of Operational Research, Elsevier, vol. 236(1), pages 200-208.
    7. Soyer, Refik & Tanyeri, Kadir, 2006. "Bayesian portfolio selection with multi-variate random variance models," European Journal of Operational Research, Elsevier, vol. 171(3), pages 977-990, June.
    8. Yu, Mei & Takahashi, Satoru & Inoue, Hiroshi & Wang, Shouyang, 2010. "Dynamic portfolio optimization with risk control for absolute deviation model," European Journal of Operational Research, Elsevier, vol. 201(2), pages 349-364, March.
    9. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    10. Bryan Kelly & Alexander Ljungqvist, 2012. "Testing Asymmetric-Information Asset Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 25(5), pages 1366-1413.
    11. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    12. Jiang Wang, 1993. "A Model of Intertemporal Asset Prices Under Asymmetric Information," Review of Economic Studies, Oxford University Press, vol. 60(2), pages 249-282.
    13. Celikyurt, U. & Ozekici, S., 2007. "Multiperiod portfolio optimization models in stochastic markets using the mean-variance approach," European Journal of Operational Research, Elsevier, vol. 179(1), pages 186-202, May.
    14. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    15. Huang, Dashan & Zhu, Shushang & Fabozzi, Frank J. & Fukushima, Masao, 2010. "Portfolio selection under distributional uncertainty: A relative robust CVaR approach," European Journal of Operational Research, Elsevier, vol. 203(1), pages 185-194, May.
    16. Mansini, Renata & Speranza, Maria Grazia, 1999. "Heuristic algorithms for the portfolio selection problem with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 114(2), pages 219-233, April.
    17. Dilip B. Madan, 2010. "Stochastic Processes in Finance," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 277-314, December.
    18. Bae, Geum Il & Kim, Woo Chang & Mulvey, John M., 2014. "Dynamic asset allocation for varied financial markets under regime switching framework," European Journal of Operational Research, Elsevier, vol. 234(2), pages 450-458.
    19. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    20. Kraft, Holger & Steffensen, Mogens, 2013. "A dynamic programming approach to constrained portfolios," European Journal of Operational Research, Elsevier, vol. 229(2), pages 453-461.
    21. Çanakoglu, Ethem & Özekici, Süleyman, 2010. "Portfolio selection in stochastic markets with HARA utility functions," European Journal of Operational Research, Elsevier, vol. 201(2), pages 520-536, March.
    22. Lin, Chang-Chun & Liu, Yi-Ting, 2008. "Genetic algorithms for portfolio selection problems with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 185(1), pages 393-404, February.
    23. Summers, Lawrence H, 1986. " Does the Stock Market Rationally Reflect Fundamental Values?," Journal of Finance, American Finance Association, vol. 41(3), pages 591-601, July.
    24. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    25. Buckley, Winston S. & Long, Hongwei, 2015. "A discontinuous mispricing model under asymmetric information," European Journal of Operational Research, Elsevier, vol. 243(3), pages 944-955.
    26. Paolo Guasoni, 2006. "Asymmetric Information in Fads Models," Finance and Stochastics, Springer, vol. 10(2), pages 159-177, April.
    27. Wang, J. & Forsyth, P.A., 2011. "Continuous time mean variance asset allocation: A time-consistent strategy," European Journal of Operational Research, Elsevier, vol. 209(2), pages 184-201, March.
    28. Corazza, Marco & Favaretto, Daniela, 2007. "On the existence of solutions to the quadratic mixed-integer mean-variance portfolio selection problem," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1947-1960, February.
    29. Hans Kellerer & Renata Mansini & M. Speranza, 2000. "Selecting Portfolios with Fixed Costs and Minimum Transaction Lots," Annals of Operations Research, Springer, vol. 99(1), pages 287-304, December.
    30. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    31. Fu, Jun & Wei, Jiaqin & Yang, Hailiang, 2014. "Portfolio optimization in a regime-switching market with derivatives," European Journal of Operational Research, Elsevier, vol. 233(1), pages 184-192.
    32. Cyrus Ramezani & Yong Zeng, 2007. "Maximum likelihood estimation of the double exponential jump-diffusion process," Annals of Finance, Springer, vol. 3(4), pages 487-507, October.
    33. Jakša Cvitanić & Vassilis Polimenis & Fernando Zapatero, 2008. "Optimal portfolio allocation with higher moments," Annals of Finance, Springer, vol. 4(1), pages 1-28, January.
    34. David Easley & Maureen O'hara, 2004. "Information and the Cost of Capital," Journal of Finance, American Finance Association, vol. 59(4), pages 1553-1583, August.
    35. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Salmeron Garrido, Jose Antonio & García Martí, Dolores & D'Auria, Bernardo, 2017. "Optimal portfolio with insider information on the stochastic interest rate," DES - Working Papers. Statistics and Econometrics. WS 25819, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Bernardo D'Auria & Jos'e Antonio Salmer'on, 2017. "Optimal portfolio with insider information on the stochastic interest rate," Papers 1711.03642, arXiv.org, revised Sep 2019.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:252:y:2016:i:2:p:676-686. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/eor .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.