IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/6994.html
   My bibliography  Save this paper

Closed-Form Approximations for Spread Option Prices and Greeks

Author

Listed:
  • Li, Minqiang

Abstract

We develop a new closed-form approximation method for pricing spread options. Numerical analysis shows that our method is more accurate than existing analytical approximations. Our method is also extremely fast, with computing time more than two orders of magnitude shorter than one-dimensional numerical integration. We also develop closed-form approximations for the greeks of spread options. In addition, we analyze the price sensitivities of spread options and provide lower and upper bounds for digital spread options. Our method enables the accurate pricing of a bulk volume of spread options with different specifications in real time, which offers traders a potential edge in financial markets. The closed-form approximations of greeks serve as valuable tools in financial applications such as dynamic hedging and value-at-risk calculations.

Suggested Citation

  • Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:6994
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/6994/1/MPRA_paper_6994.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Paul Berhanu Girma & Albert S. Paulson, 1998. "Seasonality in petroleum futures spreads," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 18(5), pages 581-598, August.
    2. Chen, Ren-Raw & Yeh, Shih-Kuo, 2002. "Analytical Upper Bounds for American Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(1), pages 117-135, March.
    3. Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(2), pages 449-473, June.
    4. Johnson, Shane A. & Tian, Yisong S., 2000. "Indexed executive stock options," Journal of Financial Economics, Elsevier, vol. 57(1), pages 35-64, July.
    5. Minqiang Li, 2008. "The impact of return nonnormality on exchange options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(9), pages 845-870, September.
    6. Chung, San-Lin & Chang, Hsieh-Chung, 2007. "Generalized Analytical Upper Bounds for American Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(1), pages 209-227, March.
    7. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    8. Perrakis, Stylianos & Ryan, Peter J, 1984. "Option Pricing Bounds in Discrete Time," Journal of Finance, American Finance Association, vol. 39(2), pages 519-525, June.
    9. Minqiang Li & Jieyun Zhou & Shi-Jie Deng, 2010. "Multi-asset spread option pricing and hedging," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 305-324.
    10. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    11. Vicky Henderson & David Hobson & William Shaw & Rafal Wojakowski, 2007. "Bounds for in-progress floating-strike Asian options using symmetry," Annals of Operations Research, Springer, vol. 151(1), pages 81-98, April.
    12. Paul Berhanu Girma & Albert S. Paulson, 1999. "Risk arbitrage opportunities in petroleum futures spreads," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(8), pages 931-955, December.
    13. Mark Grinblatt & Sheridan Titman, 1989. "Adverse Risk Incentives and the Design of Performance-Based Contracts," Management Science, INFORMS, vol. 35(7), pages 807-822, July.
    14. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    15. Robert L. Johnson & Carl R. Zulauf & Scott H. Irwin & Mary E. Gerlow, 1991. "The soybean complex spread: An examination of market efficiency from the viewpoint of a production process," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 11(1), pages 25-37, February.
    16. Geoffrey Poitras, 1998. "Spread options, exchange options, and arithmetic Brownian motion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 18(5), pages 487-517, August.
    17. 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.
    18. McDonald, Robert L & Siegel, Daniel R, 1985. "Investment and the Valuation of Firms When There Is an Option to Shut Down," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 331-349, June.
    19. Lo, Andrew W., 1987. "Semi-parametric upper bounds for option prices and expected payoffs," Journal of Financial Economics, Elsevier, vol. 19(2), pages 373-387, December.
    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. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    2. Minqiang Li & Jieyun Zhou & Shi-Jie Deng, 2010. "Multi-asset spread option pricing and hedging," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 305-324.
    3. Kwangil Bae, 2019. "Valuation and applications of compound basket options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(6), pages 704-720, June.
    4. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
    5. J. C. Arismendi & Marcel Prokopczuk, 2016. "A moment-based analytic approximation of the risk-neutral density of American options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(6), pages 409-444, November.
    6. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.
    7. Juan Arismendi, 2014. "A Multi-Asset Option Approximation for General Stochastic Processes," ICMA Centre Discussion Papers in Finance icma-dp2014-03, Henley Business School, University of Reading.
    8. Chung, San-Lin & Hung, Mao-Wei & Wang, Jr-Yan, 2010. "Tight bounds on American option prices," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 77-89, January.
    9. Chun-Sing Lau & Chi-Fai Lo, 2014. "The pricing of basket-spread options," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1971-1982, November.
    10. William R. Melick & Charles P. Thomas, 1996. "Using options prices to infer PDF'S for asset prices: an application to oil prices during the Gulf crisis," International Finance Discussion Papers 541, Board of Governors of the Federal Reserve System (U.S.).
    11. Hemantha Herath & Pranesh Kumar & Amin Amershi, 2013. "Crack spread option pricing with copulas," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 37(1), pages 100-121, January.
    12. Radnai, Márton, 2005. "Indexált alaptermék árú opciók [Indexed options based on the underlying price]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(2), pages 130-143.
    13. Donald J. Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Cowles Foundation Discussion Papers 1518, Cowles Foundation for Research in Economics, Yale University.
    14. Arismendi, Juan & Genaro, Alan De, 2016. "A Monte Carlo multi-asset option pricing approximation for general stochastic processes," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 75-99.
    15. Joel Vanden, 2006. "Exact Superreplication Strategies for a Class of Derivative Assets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 61-87.
    16. Donald Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Yale School of Management Working Papers amz2581, Yale School of Management, revised 01 Jul 2005.
    17. Kung, James J. & Lee, Lung-Sheng, 2009. "Option pricing under the Merton model of the short rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 378-386.
    18. Boyle, Phelim P. & Lin, X. Sheldon, 1997. "Bounds on contingent claims based on several assets," Journal of Financial Economics, Elsevier, vol. 46(3), pages 383-400, December.
    19. Minqiang Li & Kyuseok Lee, 2011. "An adaptive successive over-relaxation method for computing the Black-Scholes implied volatility," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1245-1269.
    20. Ye Du & Shan Xue & Yanchu Liu, 2019. "Robust upper bounds for American put options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(1), pages 3-14, January.

    More about this item

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    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:pra:mprapa:6994. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.