IDEAS home Printed from https://ideas.repec.org/a/wly/apsmbi/v31y2015i4p536-550.html
   My bibliography  Save this article

A drift‐free simulation method for pricing commodity derivatives

Author

Listed:
  • José Luis Fernández
  • Marta Pou
  • Carlos Vázquez

Abstract

Having in view the pricing of commodity derivatives in Libor Market Model (LMM) setting, we first analyze the set of basic rates we need to formulate the model by using the spanning tree concept taken from graph theory. Next, we present an efficient procedure for Monte Carlo simulation of the dynamics of the rates associated to LMM, avoiding the presence of the rates dependent drifts (drift‐free simulation) and the presence of negative deflated bond prices and negative forward rates. The method is based upon a new parameterization of the martingales introduced by Glasserman and Zhao and it is extended to a Cross‐Market Model for commodities. Finally, a particular example of commodity derivative (spread option) pricing problem is considered. Copyright © 2014 John Wiley & Sons, Ltd.

Suggested Citation

  • José Luis Fernández & Marta Pou & Carlos Vázquez, 2015. "A drift‐free simulation method for pricing commodity derivatives," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(4), pages 536-550, July.
    • Handle: RePEc:wly:apsmbi:v:31:y:2015:i:4:p:536-550
    DOI: 10.1002/asmb.2056
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/asmb.2056
    Download Restriction: no
    File URL: https://libkey.io/10.1002/asmb.2056?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
    ---><---

    References listed on IDEAS

    as
    1. S. Galluccio & J.‐M. Ly & Z. Huang & O. Scaillet, 2007. "Theory And Calibration Of Swap Market Models," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 111-141, January.
    2. Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
    3. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    4. Bryan R. Routledge & Duane J. Seppi & Chester S. Spatt, 2000. "Equilibrium Forward Curves for Commodities," Journal of Finance, American Finance Association, vol. 55(3), pages 1297-1338, June.
    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. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    7. K. F. Pilz & E. Schlögl, 2013. "A hybrid commodity and interest rate market model," Quantitative Finance, Taylor & Francis Journals, vol. 13(4), pages 543-560, March.
    8. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    9. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    10. Mikkelsen, Peter, 2001. "Cross-Currency LIBOR Market Models," Finance Working Papers 01-6, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    Full references (including those not matched with items on IDEAS)

    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. K. F. Pilz & E. Schlögl, 2013. "A hybrid commodity and interest rate market model," Quantitative Finance, Taylor & Francis Journals, vol. 13(4), pages 543-560, March.
    2. Raoul Pietersz & Marcel Regenmortel, 2006. "Generic market models," Finance and Stochastics, Springer, vol. 10(4), pages 507-528, December.
      • Pietersz, R. & van Regenmortel, M., 2005. "Generic Market Models," ERIM Report Series Research in Management ERS-2005-010-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
      • Raoul Pietersz & Marcel van Regenmortel, 2005. "Generic Market Models," Finance 0502009, University Library of Munich, Germany.
    3. P. Karlsson & K. F. Pilz & E. Schlögl, 2017. "Calibrating a market model with stochastic volatility to commodity and interest rate risk," Quantitative Finance, Taylor & Francis Journals, vol. 17(6), pages 907-925, June.
    4. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    5. Frank De Jong & Joost Driessen & Antoon Pelsser, 2001. "Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis," Review of Finance, European Finance Association, vol. 5(3), pages 201-237.
    6. Sven Rady, 1997. "Option pricing in the presence of natural boundaries and a quadratic diffusion term (*)," Finance and Stochastics, Springer, vol. 1(4), pages 331-344.
    7. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    8. Bisht Deepak & Laha, A. K., 2017. "Pricing Option on Commodity Futures under String Shock," IIMA Working Papers WP 2017-07-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    9. Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2011. "Efficient and accurate log-Lévi approximations to Lévi driven LIBOR models," CREATES Research Papers 2011-22, Department of Economics and Business Economics, Aarhus University.
    10. Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2011. "Efficient and accurate log-L\'evy approximations to L\'evy driven LIBOR models," Papers 1106.0866, arXiv.org, revised Jan 2012.
    11. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, July-Dece.
    12. Munk, Claus, 2015. "Financial Asset Pricing Theory," OUP Catalogue, Oxford University Press, number 9780198716457.
    13. Ernst Eberlein & Fehmi Özkan, 2005. "The Lévy LIBOR model," Finance and Stochastics, Springer, vol. 9(3), pages 327-348, July.
    14. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    15. Patrik Karlsson & Kay F Pilz & Erik Schlogl, 2016. "Calibrating Market Model to Commodity and Interest Rate Risk," Research Paper Series 372, Quantitative Finance Research Centre, University of Technology, Sydney.
    16. Dempster, M.A.H. & Medova, Elena & Tang, Ke, 2008. "Long term spread option valuation and hedging," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2530-2540, December.
    17. Akihiko Takahashi & Kohta Takehara, 2007. "An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(1), pages 69-121, March.
    18. Secomandi, Nicola & Seppi, Duane J., 2014. "Real Options and Merchant Operations of Energy and Other Commodities," Foundations and Trends(R) in Technology, Information and Operations Management, now publishers, vol. 6(3-4), pages 161-331, July.
    19. Antonis Papapantoleon, 2010. "Old and new approaches to LIBOR modeling," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 257-275.
    20. Unterschultz, James R., 2000. "New Instruments For Co-Ordination And Risk Sharing Within The Canadian Beef Industry," Project Report Series 24046, University of Alberta, Department of Resource Economics and Environmental Sociology.

    More about this item

    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:wly:apsmbi:v:31:y:2015:i:4:p:536-550. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1526-4025 .

    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.