IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v164y2008i1p139-16510.1007-s10479-008-0398-y.html
   My bibliography  Save this article

A class of portfolio selection with a four-factor futures price model

Author

Listed:
  • Wei Yan
  • Shurong Li

Abstract

Considering the stochastic exchange rate, a four-factor futures model with the underling asset, convenience yield, instantaneous risk free interest rate and exchange rate, is established. These processes follow jump-diffusion processes (Weiner process and Poisson process). The corresponding partial differential equation (PDE) of the futures price is derived. The general solution of the PDE with parameters is drawn. The weight least squares approach is applied to obtain the parameters of above PDE. Variance is substituted by semi-variance in Markowitzs portfolio selection model. Therefore, a class of multi-period semi-variance model is formulated originally. Then, a continuous-time mean-variance portfolio model is also considered. The corresponding stochastic Hamilton-Jacobi-Bellman (HJB) equation of the problem with nonlinear constraints is derived. A numerical algorithm is proposed for finding the optimal solution in this paper. Finally, in order to demonstrate the effectiveness of the theoretical models and numerical methods, the fuel futures in Shanghai exchange market and the Brent crude oil futures in London exchange market are selected to be examples. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Wei Yan & Shurong Li, 2008. "A class of portfolio selection with a four-factor futures price model," Annals of Operations Research, Springer, vol. 164(1), pages 139-165, November.
    • Handle: RePEc:spr:annopr:v:164:y:2008:i:1:p:139-165:10.1007/s10479-008-0398-y
    DOI: 10.1007/s10479-008-0398-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0398-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0398-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    2. Paul A. Samuelson, 2011. "Lifetime Portfolio Selection by Dynamic Stochastic Programming," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 31, pages 465-472, World Scientific Publishing Co. Pte. Ltd..
    3. Hogan, William W. & Warren, James M., 1974. "Toward the Development of an Equilibrium Capital-Market Model Based on Semivariance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(1), pages 1-11, January.
    4. Robert R. Grauer & Nils H. Hakansson, 1993. "On the Use of Mean-Variance and Quadratic Approximations in Implementing Dynamic Investment Strategies: A Comparison of Returns and Investment Policies," Management Science, INFORMS, vol. 39(7), pages 856-871, July.
    5. Gibson, Rajna & Schwartz, Eduardo S, 1990. "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    6. 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.
    7. MOSSIN, Jan, 1968. "Optimal multiperiod portfolio policies," LIDAM Reprints CORE 19, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
    9. Wenjing Guo & Chengming Xu, 2004. "Optimal portfolio selection when stock prices follow an jump-diffusion process," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(3), pages 485-496, December.
    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. Sabri Boubaker & Zhenya Liu & Yaosong Zhan, 2022. "Risk management for crude oil futures: an optimal stopping-timing approach," Annals of Operations Research, Springer, vol. 313(1), pages 9-27, June.
    2. Junhe Chen & Marcos Escobar-Anel, 2021. "Model uncertainty on commodity portfolios, the role of convenience yield," Annals of Finance, Springer, vol. 17(4), pages 501-528, December.
    3. Taras Bodnar & Nestor Parolya & Wolfgang Schmid, 2015. "A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function," Annals of Operations Research, Springer, vol. 229(1), pages 121-158, June.
    4. Jun Deng & Huifeng Pan & Shuyu Zhang & Bin Zou, 2021. "Optimal Bitcoin trading with inverse futures," Annals of Operations Research, Springer, vol. 304(1), pages 139-163, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Xili & Zhang, Weiguo & Xiao, Weilin, 2013. "Multi-period portfolio optimization under possibility measures," Economic Modelling, Elsevier, vol. 35(C), pages 401-408.
    2. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    3. Guedes, José & Santos, Pedro, 2016. "Valuing an offshore oil exploration and production project through real options analysis," Energy Economics, Elsevier, vol. 60(C), pages 377-386.
    4. Moreno, Manuel & Novales, Alfonso & Platania, Federico, 2019. "Long-term swings and seasonality in energy markets," European Journal of Operational Research, Elsevier, vol. 279(3), pages 1011-1023.
    5. Nguyen, Duc Binh Benno & Prokopczuk, Marcel, 2019. "Jumps in commodity markets," Journal of Commodity Markets, Elsevier, vol. 13(C), pages 55-70.
    6. Penikas, Henry, 2010. "Copula-Models in Foreign Exchange Risk-Management of a Bank," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 17(1), pages 62-87.
    7. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, October.
    8. Stephen Foerster & Juhani T. Linnainmaa & Brian T. Melzer & Alessandro Previtero, 2017. "Retail Financial Advice: Does One Size Fit All?," Journal of Finance, American Finance Association, vol. 72(4), pages 1441-1482, August.
    9. repec:idb:brikps:365 is not listed on IDEAS
    10. Insley, M.C. & Wirjanto, T.S., 2010. "Contrasting two approaches in real options valuation: Contingent claims versus dynamic programming," Journal of Forest Economics, Elsevier, vol. 16(2), pages 157-176, April.
    11. Wang, Yuanrong & Aste, Tomaso, 2023. "Dynamic portfolio optimization with inverse covariance clustering," LSE Research Online Documents on Economics 117701, London School of Economics and Political Science, LSE Library.
    12. Max F. Schöne & Stefan Spinler, 2017. "A four-factor stochastic volatility model of commodity prices," Review of Derivatives Research, Springer, vol. 20(2), pages 135-165, July.
    13. Davi Valladão & Thuener Silva & Marcus Poggi, 2019. "Time-consistent risk-constrained dynamic portfolio optimization with transactional costs and time-dependent returns," Annals of Operations Research, Springer, vol. 282(1), pages 379-405, November.
    14. Klos, Alexander, 2004. "The investment horizon and dynamic asset allocation--some experimental evidence," Economics Letters, Elsevier, vol. 85(2), pages 167-170, November.
    15. Servaas van Bilsen & Roger J. A. Laeven & Theo E. Nijman, 2020. "Consumption and Portfolio Choice Under Loss Aversion and Endogenous Updating of the Reference Level," Management Science, INFORMS, vol. 66(9), pages 3927-3955, September.
    16. Nikolay Gospodinov & Ibrahim Jamali, 2018. "Monetary policy uncertainty, positions of traders and changes in commodity futures prices," European Financial Management, European Financial Management Association, vol. 24(2), pages 239-260, March.
    17. Kai Barron, 2021. "Belief updating: does the ‘good-news, bad-news’ asymmetry extend to purely financial domains?," Experimental Economics, Springer;Economic Science Association, vol. 24(1), pages 31-58, March.
    18. Benjamin M. Friedman, 1980. "The Effect of Shifting Wealth Ownership on the Term Structure of Interest Rates," NBER Working Papers 0239, National Bureau of Economic Research, Inc.
    19. Richter, Martin & Sørensen, Carsten, 2002. "Stochastic Volatility and Seasonality in Commodity Futures and Options: The Case of Soybeans," Working Papers 2002-4, Copenhagen Business School, Department of Finance.
    20. Chris Brooks & Marcel Prokopczuk, 2013. "The dynamics of commodity prices," Quantitative Finance, Taylor & Francis Journals, vol. 13(4), pages 527-542, March.
    21. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.

    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:spr:annopr:v:164:y:2008:i:1:p:139-165:10.1007/s10479-008-0398-y. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.