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Closed form spread option valuation

Author

Listed:
  • Bjerksund, Petter

    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

  • Stensland, Gunnar

    (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

Abstract

This paper considers the valuation of a spread call when asset prices are lognormal. The implicit strategy of the Kirk formula is to exercise if the price of the long asset exceeds a given power function of the price of the short asset. We derive a formula for the spread call value, conditional on following this feasible but non-optimal exercise strategy. Numerical investigations indicate that the lower bound produced by our formula is extremely accurate. The precision is much higher than the Kirk formula. Moreover, optimizing with respect to the strategy parameters (which corresponds to the Carmona-Durrleman procedure) yields only a marginal improvement of accuracy (if any).

Suggested Citation

  • Bjerksund, Petter & Stensland, Gunnar, 2006. "Closed form spread option valuation," Discussion Papers 2006/20, Norwegian School of Economics, Department of Business and Management Science.
    • Handle: RePEc:hhs:nhhfms:2006_020
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    File URL: http://hdl.handle.net/11250/164108
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    Citations

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    Cited by:

    1. Edward P. C. Kao & Weiwei Xie, 2017. "Pricing spread options by generalized bivariate edgeworth expansion," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-30, June.
    2. Elisa Alòs & Jorge A. León, 2016. "On the short-maturity behaviour of the implied volatility skew for random strike options and applications to option pricing approximation," Quantitative Finance, Taylor & Francis Journals, vol. 16(1), pages 31-42, January.
    3. Elisa Alòs & Jorge A. León, 2013. "On the closed-form approximation of short-time random strike options," Economics Working Papers 1347, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Jing Li & Lingfei Li & Rafael Mendoza-Arriaga, 2016. "Additive subordination and its applications in finance," Finance and Stochastics, Springer, vol. 20(3), pages 589-634, July.
    5. Tommaso Paletta & Arturo Leccadito & Radu Tunaru, 2013. "Pricing and Hedging Basket Options with Exact Moment Matching," Papers 1312.4443, arXiv.org.
    6. Gerald H. L. Cheang & Len Patrick Dominic M. Garces, 2020. "Representation of Exchange Option Prices under Stochastic Volatility Jump-Diffusion Dynamics," Papers 2002.10202, arXiv.org.
    7. Dongdong Hu & Hasanjan Sayit & Svetlozar T. Rachev, 2021. "Moment Matching Method for Pricing Spread Options with Mean-Variance Mixture L\'evy Motions," Papers 2109.02872, arXiv.org, revised Feb 2024.
    8. Chris Kenyon & Mourad Berrahoui & Benjamin Poncet, 2017. "Counterparty Trading Limits Revisited:CSAs, IM, SwapAgent(r), from PFE to PFL," Papers 1710.03161, arXiv.org, revised Nov 2018.
    9. Edoardo Berton & Lorenzo Mercuri, 2021. "An Efficient Unified Approach for Spread Option Pricing in a Copula Market Model," Papers 2112.11968, arXiv.org, revised Feb 2023.
    10. Matteo Gardini & Piergiacomo Sabino, 2022. "Exchange option pricing under variance gamma-like models," Papers 2207.00453, arXiv.org.
    11. Green, Rikard, 2015. "No 2015:3 Closed Form Valuation of Three-Asset Spread Options With a view towards Clean Dark Spreads," Knut Wicksell Working Paper Series 2015/3, Lund University, Knut Wicksell Centre for Financial Studies.
    12. Bertrand Tavin & Lorenz Schneider, 2018. "From the Samuelson volatility effect to a Samuelson correlation effect : An analysis of crude oil calendar spread options," Post-Print hal-02311970, HAL.
    13. Stefano Herzel & Marco Nicolosi, 2019. "Optimal strategies with option compensation under mean reverting returns or volatilities," Computational Management Science, Springer, vol. 16(1), pages 47-69, February.
    14. Lahrech, Mohamed Taha & Benabdellah, Majid & Dehhaoui, Mohammed & Benchekroun, Fayçal, 2018. "Evaluation des options financières : revue de littérature et explication intuitive des méthodes de calcul [Evaluation of financial options: literature review and intuitive explanation of the calcul," MPRA Paper 95486, University Library of Munich, Germany.
    15. Lorenz Schneider & Bertrand Tavin, 2014. "From the Samuelson Volatility Effect to a Samuelson Correlation Effect: Evidence from Crude Oil Calendar Spread Options," Papers 1401.7913, arXiv.org, revised Feb 2015.
    16. Alexandre Petkovic, 2009. "Three essays on exotic option pricing, multivariate Lévy processes and linear aggregation of panel models," ULB Institutional Repository 2013/210357, ULB -- Universite Libre de Bruxelles.
    17. Griselda Deelstra & Alexandre Petkovic & Michèle Vanmaele, 2008. "Pricing and Hedging Asian Basket Spread Options," Working Papers ECARES 2008_004, ULB -- Universite Libre de Bruxelles.
    18. Nuerxiati Abudurexiti & Kai He & Dongdong Hu & Hasanjan Sayit, 2021. "A note on closed-form spread option valuation under log-normal models," Papers 2109.05431, arXiv.org, revised Feb 2024.

    More about this item

    Keywords

    Spread option; closed form; valuation formula; lognormal asset prices;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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