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Multi-asset Spread Option Pricing and Hedging


  • Li, Minqiang
  • Deng, Shijie
  • Zhou, Jieyun


We provide two new closed-form approximation methods for pricing spread options on a basket of risky assets: the extended Kirk approximation and the second-order boundary approximation. Numerical analysis shows that while the latter method is more accurate than the former, both methods are extremely fast and accurate. Approximations for important Greeks are also derived in closed form. Our approximation methods enable the accurate pricing of a bulk volume of spread options on a large number of assets in real time, which offers traders a potential edge in a dynamic market environment.

Suggested Citation

  • Li, Minqiang & Deng, Shijie & Zhou, Jieyun, 2008. "Multi-asset Spread Option Pricing and Hedging," MPRA Paper 8259, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:8259

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    References listed on IDEAS

    1. 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.
    2. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    3. 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..
    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. 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.
    6. 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.
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    Cited by:

    1. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    2. Tommaso Paletta & Arturo Leccadito & Radu Tunaru, 2013. "Pricing and Hedging Basket Options with Exact Moment Matching," Papers 1312.4443,
    3. Li, Minqiang & Mercurio, Fabio, 2013. "Closed-Form Approximation of Timer Option Prices under General Stochastic Volatility Models," MPRA Paper 47465, University Library of Munich, Germany.
    4. Leccadito, Arturo & Paletta, Tommaso & Tunaru, Radu, 2016. "Pricing and hedging basket options with exact moment matching," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 59-69.
    5. Farkas, Walter & Gourier, Elise & Huitema, Robert & Necula, Ciprian, 2017. "A two-factor cointegrated commodity price model with an application to spread option pricing," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 249-268.
    6. 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.
    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, Reading University.
    8. Romain Bompis, 2017. "Weak approximations for arithmetic means of geometric Brownian motions and applications to Basket options," Working Papers hal-01502886, HAL.
    9. Olivares Pablo & Villamor Enrique, 2017. "Valuing Exchange Options Under an Ornstein-Uhlenbeck Covariance Model," Papers 1711.10013,
    10. repec:taf:apmtfi:v:23:y:2016:i:6:p:409-444 is not listed on IDEAS
    11. Pablo Olivares, 2014. "Pricing of Basket Options Using Polynomial Approximations," Papers 1404.3160,
    12. Nicola Cufaro Petroni & Piergiacomo Sabino, 2015. "Cointegrating Jumps: an Application to Energy Facilities," Papers 1509.01144,, revised Jul 2016.
    13. Pablo Olivares & Alexander Alvarez, 2014. "A Note on the Pricing of Basket Options Using Taylor Approximations," Papers 1404.3229,
    14. Pellegrino, Tommaso & Sabino, Piergiacomo, 2014. "On the use of the moment-matching technique for pricing and hedging multi-asset spread options," Energy Economics, Elsevier, vol. 45(C), pages 172-185.

    More about this item


    multi-asset spread option; closed-form approximation;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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