IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v18y2014i2p407-430.html
   My bibliography  Save this article

Optimal portfolios in commodity futures markets

Author

Listed:
  • Fred Benth
  • Jukka Lempa

Abstract

We develop a general approach to portfolio optimization in futures markets. Following the Heath–Jarrow–Morton (HJM) approach, we model the entire futures price curve at once as a solution of a stochastic partial differential equation. We also develop a general formalism to handle portfolios of futures contracts. In the portfolio optimization problem, the agent invests in futures contracts and a risk-free asset, and her objective is to maximize the utility from final wealth. In order to capture self-consistent futures price dynamics, we study a class of futures price curve models which admit a finite-dimensional realization. More precisely, we establish conditions under which the futures price dynamics can be realized in finite dimensions. Using the finite-dimensional realization, we derive a finite-dimensional form of the portfolio optimization problem and study its solution. We also give an economic interpretation of the coordinate process driving the finite-dimensional realization. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Fred Benth & Jukka Lempa, 2014. "Optimal portfolios in commodity futures markets," Finance and Stochastics, Springer, vol. 18(2), pages 407-430, April.
    • Handle: RePEc:spr:finsto:v:18:y:2014:i:2:p:407-430
    DOI: 10.1007/s00780-013-0224-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00780-013-0224-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00780-013-0224-5?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ivar Ekeland & Erik Taflin, 2003. "A theory of bond portfolios," Papers math/0301278, arXiv.org, revised May 2005.
    2. Tomas Björk & Lars Svensson, 2001. "On the Existence of Finite‐Dimensional Realizations for Nonlinear Forward Rate Models," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 205-243, April.
    3. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    4. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    5. repec:dau:papers:123456789/6041 is not listed on IDEAS
    6. 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.
    7. Camilla Landén & Tomas Björk, 2002. "On the construction of finite dimensional realizations for nonlinear forward rate models," Finance and Stochastics, Springer, vol. 6(3), pages 303-331.
    8. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    9. Nathanael Ringer & Michael Tehranchi, 2006. "Optimal portfolio choice in the bond market," Finance and Stochastics, Springer, vol. 10(4), pages 553-573, December.
    10. Benth, Fred Espen & Cartea, Álvaro & Kiesel, Rüdiger, 2008. "Pricing forward contracts in power markets by the certainty equivalence principle: Explaining the sign of the market risk premium," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2006-2021, October.
    11. Hans Buehler, 2006. "Consistent Variance Curve Models," Finance and Stochastics, Springer, vol. 10(2), pages 178-203, April.
    12. Tomas Björk & Magnus Blix & Camilla Landén, 2006. "On Finite Dimensional Realizations For The Term Structure Of Futures Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 281-314.
    13. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
    14. Tomas BjÃrk & Andrea Gombani, 1999. "Minimal realizations of interest rate models," Finance and Stochastics, Springer, vol. 3(4), pages 413-432.
    15. Hans Buehler, 2006. "Consistent Variance Curve Models," Finance and Stochastics, Springer, vol. 10(2), pages 178-203, April.
    16. Dennis Frestad & Fred Espen Benth & Steen Koekebakker, 2010. "Modeling Term Structure Dynamics in the Nordic Electricity Swap Market," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2), pages 53-86.
    17. Benth, Fred Espen & Koekebakker, Steen, 2008. "Stochastic modeling of financial electricity contracts," Energy Economics, Elsevier, vol. 30(3), pages 1116-1157, May.
    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. Fred Espen Benth & Paul Kruhner, 2015. "Approximation of forward curve models in commodity markets with arbitrage-free finite dimensional models," Papers 1512.05983, arXiv.org.
    2. Fred Espen Benth & Paul Kruhner, 2014. "Derivatives pricing in energy markets: an infinite dimensional approach," Papers 1412.7943, arXiv.org.
    3. Fred Espen Benth & Paul Kruhner, 2014. "Representation of infinite dimensional forward price models in commodity markets," Papers 1403.4111, arXiv.org.
    4. Charles Shaw, 2022. "Portfolio Diversification Revisited," Papers 2204.13398, arXiv.org.
    5. Fred Espen Benth & Paul Krühner, 2018. "Approximation of forward curve models in commodity markets with arbitrage-free finite-dimensional models," Finance and Stochastics, Springer, vol. 22(2), pages 327-366, April.
    6. Benth, Fred Espen & Paraschiv, Florentina, 2016. "A Structural Model for Electricity Forward Prices," Working Papers on Finance 1611, University of St. Gallen, School of Finance.
    7. Benth, Fred Espen & Paraschiv, Florentina, 2018. "A space-time random field model for electricity forward prices," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 203-216.
    8. 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.

    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. Deschatre, Thomas & Féron, Olivier & Gruet, Pierre, 2021. "A survey of electricity spot and futures price models for risk management applications," Energy Economics, Elsevier, vol. 102(C).
    2. Fred Espen Benth & Paul Kruhner, 2014. "Representation of infinite dimensional forward price models in commodity markets," Papers 1403.4111, arXiv.org.
    3. Iván Blanco, Juan Ignacio Peña, and Rosa Rodriguez, 2018. "Modelling Electricity Swaps with Stochastic Forward Premium Models," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    4. Cheng, Benjamin & Nikitopoulos, Christina Sklibosios & Schlögl, Erik, 2018. "Pricing of long-dated commodity derivatives: Do stochastic interest rates matter?," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 148-166.
    5. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    6. 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.
    7. Yalc{c}in Aktar & Erik Taflin, 2014. "A remark on smooth solutions to a stochastic control problem with a power terminal cost function and stochastic volatilities," Papers 1405.3566, arXiv.org.
    8. Olivier Feron & Pierre Gruet, 2020. "Estimation of the number of factors in a multi-factorial Heath-Jarrow-Morton model in electricity markets," Working Papers hal-02880824, HAL.
    9. Benth, Fred Espen & Paraschiv, Florentina, 2016. "A Structural Model for Electricity Forward Prices," Working Papers on Finance 1611, University of St. Gallen, School of Finance.
    10. Eckhard Platen & Stefan Tappe, 2011. "Affine Realizations for Levy Driven Interest Rate Models with Real-World Forward Rate Dynamics," Research Paper Series 289, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Anh Ngoc Lai & Constantin Mellios, 2016. "Valuation of commodity derivatives with an unobservable convenience yield," Post-Print halshs-01183166, HAL.
    12. Benth, Fred Espen & Paraschiv, Florentina, 2018. "A space-time random field model for electricity forward prices," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 203-216.
    13. Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & Tô, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, vol. 40(C), pages 989-1000.
    14. Tomas Björk & Magnus Blix & Camilla Landén, 2006. "On Finite Dimensional Realizations For The Term Structure Of Futures Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 281-314.
    15. Back, Janis & Prokopczuk, Marcel & Rudolf, Markus, 2013. "Seasonality and the valuation of commodity options," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 273-290.
    16. Virmani, Vineet, 2014. "Model Risk in Pricing Path-dependent Derivatives: An Illustration," IIMA Working Papers WP2014-03-22, Indian Institute of Management Ahmedabad, Research and Publication Department.
    17. Gourieroux, C. & Monfort, A. & Sufana, R., 2010. "International money and stock market contingent claims," Journal of International Money and Finance, Elsevier, vol. 29(8), pages 1727-1751, December.
    18. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    19. Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos-Sklibosios, 2010. "Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility," Research Paper Series 283, Quantitative Finance Research Centre, University of Technology, Sydney.
    20. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6, July-Dece.

    More about this item

    Keywords

    Futures contract; Commodity markets; Optimal portfolios; Stochastic partial differential equations; Finite-dimensional realization; Invariant foliation; 91G10; 60H15; G11; G13; C61;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    Statistics

    Access and download statistics

    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:finsto:v:18:y:2014:i:2:p:407-430. 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.