IDEAS home Printed from https://ideas.repec.org/a/eee/eneeco/v36y2013icp97-107.html
   My bibliography  Save this article

Minimal variance hedging of natural gas derivatives in exponential Lévy models: Theory and empirical performance

Author

Listed:
  • Ewald, Christian-Oliver
  • Nawar, Roy
  • Siu, Tak Kuen

Abstract

We consider the problem of hedging European options written on natural gas futures, in a market where prices of traded assets exhibit jumps, by trading in the underlying asset. We provide a general expression for the hedging strategy which minimizes the variance of the terminal hedging error, in terms of stochastic integral representations of the payoffs of the options involved. This formula is then applied to compute hedge ratios for common options in various models with jumps, leading to easily computable expressions. As a benchmark we take the standard Black–Scholes and Merton delta hedges. We show that in natural gas option markets minimal variance hedging with underlying consistently outperform the benchmarks by quite a margin.

Suggested Citation

  • Ewald, Christian-Oliver & Nawar, Roy & Siu, Tak Kuen, 2013. "Minimal variance hedging of natural gas derivatives in exponential Lévy models: Theory and empirical performance," Energy Economics, Elsevier, vol. 36(C), pages 97-107.
    • Handle: RePEc:eee:eneeco:v:36:y:2013:i:c:p:97-107
    DOI: 10.1016/j.eneco.2012.12.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0140988312003295
    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. Krichene, Noureddine, 2002. "World crude oil and natural gas: a demand and supply model," Energy Economics, Elsevier, vol. 24(6), pages 557-576, November.
    3. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    4. repec:spr:compst:v:51:y:2000:i:2:p:315-339 is not listed on IDEAS
    5. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
    6. Lamberton, Damien & Pham, Huyên & Schweizer, Martin, 1998. "Local risk-minimization under transaction costs," SFB 373 Discussion Papers 1998,18, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, July.
    8. Litzenberger, Robert H & Rabinowitz, Nir, 1995. "Backwardation in Oil Futures Markets: Theory and Empirical Evidence," Journal of Finance, American Finance Association, vol. 50(5), pages 1517-1545, December.
    9. Bouleau, Nicolas & Lamberton, Damien, 1989. "Residual risks and hedging strategies in Markovian markets," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 131-150, October.
    10. repec:dau:papers:123456789/607 is not listed on IDEAS
    11. Alexander, Carol & Prokopczuk, Marcel & Sumawong, Anannit, 2013. "The (de)merits of minimum-variance hedging: Application to the crack spread," Energy Economics, Elsevier, vol. 36(C), pages 698-707.
    12. Rolf Poulsen & Klaus Reiner Schenk-Hoppe & Christian-Oliver Ewald, 2009. "Risk minimization in stochastic volatility models: model risk and empirical performance," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 693-704.
    13. Fred Espen Benth & Giulia Di Nunno & Arne Løkka & Bernt Øksendal & Frank Proske, 2003. "Explicit Representation of the Minimal Variance Portfolio in Markets Driven by Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 55-72, January.
    14. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    15. Huyên Pham, 2000. "On quadratic hedging in continuous time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 315-339, April.
    16. Hélyette Geman & Dilip B. Madan & Marc Yor, 2001. "Time Changes for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 79-96, January.
    17. Christopher L. Culp & Merton H. Miller, 1995. "Hedging In The Theory Of Corporate Finance: A Reply To Our Critics," Journal of Applied Corporate Finance, Morgan Stanley, vol. 8(1), pages 121-128, March.
    18. Takuji Arai, 2005. "An extension of mean-variance hedging to the discontinuous case," Finance and Stochastics, Springer, vol. 9(1), pages 129-139, January.
    19. Helyette Geman, 2005. "Commodities and Commodity Derivatives. Modeling and Pricing for Agriculturals, Metals and Energy," Post-Print halshs-00144182, HAL.
    20. 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. Takuji Arai & Yuto Imai & Ryoichi Suzuki, 2016. "Numerical Analysis On Local Risk-Minimization For Exponential Lévy Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-27, March.
    2. Takuji Arai & Yuto Imai & Ryoichi Suzuki, 2015. "Numerical analysis on local risk-minimization forexponential L\'evy models," Papers 1506.03898, arXiv.org.

    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. Geman, Helyette, 2002. "Pure jump Levy processes for asset price modelling," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1297-1316, July.
    2. Cl'ement M'enass'e & Peter Tankov, 2015. "Asymptotic indifference pricing in exponential L\'evy models," Papers 1502.03359, arXiv.org, revised Feb 2015.
    3. Yanhui Mi, 2016. "A modified stochastic volatility model based on Gamma Ornstein–Uhlenbeck process and option pricing," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 1-16, June.
    4. Wendong Zheng & Chi Hung Yuen & Yue Kuen Kwok, 2016. "Recursive Algorithms For Pricing Discrete Variance Options And Volatility Swaps Under Time-Changed Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-29, March.
    5. Jose Cruz & Daniel Sevcovic, 2020. "On solutions of a partial integro-differential equation in Bessel potential spaces with applications in option pricing models," Papers 2003.03851, arXiv.org.
    6. Yongxin Yang & Yu Zheng & Timothy M. Hospedales, 2016. "Gated Neural Networks for Option Pricing: Rationality by Design," Papers 1609.07472, arXiv.org, revised Mar 2020.
    7. Zura Kakushadze, 2016. "Volatility Smile as Relativistic Effect," Papers 1610.02456, arXiv.org, revised Feb 2017.
    8. Yacine Aït-Sahalia & Jean Jacod, 2012. "Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data," Journal of Economic Literature, American Economic Association, vol. 50(4), pages 1007-1050, December.
    9. Li, Minqiang, 2008. "Price Deviations of S&P 500 Index Options from the Black-Scholes Formula Follow a Simple Pattern," MPRA Paper 11530, University Library of Munich, Germany.
    10. 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.
    11. Shuang Li & Yanli Zhou & Yonghong Wu & Xiangyu Ge, 2017. "Equilibrium approach of asset and option pricing under Lévy process and stochastic volatility," Australian Journal of Management, Australian School of Business, vol. 42(2), pages 276-295, May.
    12. Bakshi, Gurdip & Panayotov, George, 2010. "First-passage probability, jump models, and intra-horizon risk," Journal of Financial Economics, Elsevier, vol. 95(1), pages 20-40, January.
    13. Kao, Lie-Jane & Wu, Po-Cheng & Lee, Cheng-Few, 2012. "Time-changed GARCH versus the GARJI model for prediction of extreme news events: An empirical study," International Review of Economics & Finance, Elsevier, vol. 21(1), pages 115-129.
    14. Madan, Dilip B. & Wang, King, 2016. "Nonrandom price movements," Finance Research Letters, Elsevier, vol. 17(C), pages 103-109.
    15. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    16. Erdemlioglu, Deniz & Laurent, Sébastien & Neely, Christopher J., 2015. "Which continuous-time model is most appropriate for exchange rates?," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 256-268.
    17. Feng, Chengxiao & Tan, Jie & Jiang, Zhenyu & Chen, Shuang, 2020. "A generalized European option pricing model with risk management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    18. Ballotta, Laura & Deelstra, Griselda & Rayée, Grégory, 2017. "Multivariate FX models with jumps: Triangles, Quantos and implied correlation," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1181-1199.
    19. Svetlana Boyarchenko & Sergei Levendorskiĭ, 2019. "Sinh-Acceleration: Efficient Evaluation Of Probability Distributions, Option Pricing, And Monte Carlo Simulations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-49, May.
    20. Colino, Jesús P., 2008. "New stochastic processes to model interest rates : LIBOR additive processes," DES - Working Papers. Statistics and Econometrics. WS ws085316, Universidad Carlos III de Madrid. Departamento de Estadística.

    More about this item

    Keywords

    Quadratic hedging; Jump-diffusion models; Natural gas options; Energy derivatives; Resource economics;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • Q49 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Other

    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:eee:eneeco:v:36:y:2013:i:c:p:97-107. 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: (Haili He). General contact details of provider: http://www.elsevier.com/locate/eneco .

    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.