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A general closed-form spread option pricing formula

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  • Caldana, Ruggero
  • Fusai, Gianluca
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    Abstract

    We propose a new accurate method for pricing European spread options by extending the lower bound approximation of Bjerksund and Stensland (2011) beyond the classical Black–Scholes framework. This is possible via a procedure requiring a univariate Fourier inversion. In addition, we are also able to obtain a new tight upper bound. Our method provides also an exact closed form solution via Fourier inversion of the exchange option price, generalizing the Margrabe (1978) formula. The method is applicable to models in which the joint characteristic function of the underlying assets forming the spread is known analytically. We test the performance of these new pricing algorithms performing numerical experiments on different stochastic dynamic models.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Banking & Finance.

    Volume (Year): 37 (2013)
    Issue (Month): 12 ()
    Pages: 4893-4906

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    Handle: RePEc:eee:jbfina:v:37:y:2013:i:12:p:4893-4906

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    Web page: http://www.elsevier.com/locate/jbf

    Related research

    Keywords: Spread option; Exchange option; Stochastic process; Characteristic function; Fourier inversion; Control variate;

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    References

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    1. Peter Laurence & Tai-Ho Wang, 2008. "Distribution-free upper bounds for spread options and market-implied antimonotonicity gap," The European Journal of Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 14(8), pages 717-734.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    3. Dilip Madan, 2009. "Capital requirements, acceptable risks and profits," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 9(7), pages 767-773.
    4. Gerald Cheang & Carl Chiarella, 2011. "Exchange Options Under Jump-Diffusion Dynamics," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 18(3), pages 245-276.
    5. Álvaro Cartea & Carlos González-Pedraz, 2010. "How much should we pay for interconnecting electricity markets? A real options approach," Business Economics Working Papers, Universidad Carlos III, Departamento de Economía de la Empresa wb103206, Universidad Carlos III, Departamento de Economía de la Empresa.
    6. Dempster, M.A.H. & Medova, Elena & Tang, Ke, 2008. "Long term spread option valuation and hedging," Journal of Banking & Finance, Elsevier, Elsevier, vol. 32(12), pages 2530-2540, December.
    7. Ben Hambly & Sam Howison & Tino Kluge, 2009. "Modelling spikes and pricing swing options in electricity markets," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 9(8), pages 937-949.
    8. Aanand Venkatramanan & Carol Alexander, 2011. "Closed Form Approximations for Spread Options," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 18(5), pages 447-472, January.
    9. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, American Finance Association, vol. 33(1), pages 177-86, March.
    10. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    11. Duan, Jin-Chuan & Pliska, Stanley R., 2004. "Option valuation with co-integrated asset prices," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 28(4), pages 727-754, January.
    12. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    13. Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 38(02), pages 449-473, June.
    14. Ernst Eberlein & Dilip B. Madan, 2012. "Unbounded liabilities, capital reserve requirements and the taxpayer put option," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 12(5), pages 709-724, October.
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    Cited by:
    1. Christa Cuchiero & Claudio Fontana & Alessandro Gnoatto, 2014. "A general HJM framework for multiple yield curve modeling," Papers 1406.4301, arXiv.org.

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