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On the use of the moment-matching technique for pricing and hedging multi-asset spread options

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  • Pellegrino, Tommaso
  • Sabino, Piergiacomo

Abstract

The aim of this paper is to show the benefit of applying a moment matching technique to the short leg component in order to price and hedge multi-asset spread options: in particular, we approximate the real dynamics of the short leg component by taking a log-normal proxy, whose equivalent volatility can be computed by performing a two-moment matching approximation. The pricing of the option is then performed once the equivalent correlation parameter between the long leg underlying and the proxy short leg component has been calculated. The main advantage associated with the moment matching approach proposed in this paper is a reduction of the dimension of the pricing problem: we can, indeed, continue using all the option formulas available in the literature for two-legged spread options, i.e. spread options written on two underlyings. Besides it, the combined use of an option formula for two-legged spread options and the moment matching technique applied to the short leg component provides a good approximation to the Monte Carlo simulation. It is well-known that the Monte Carlo price and Greeks can be considered as the benchmark since no exact formula is available for the pricing and hedging of multi-asset spread options. The accuracy of our approach is even comparable to the one provided by using closed form approximation formulas based on three underlyings, where each underlying entering into the short leg component is treated separately.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:eneeco:v:45:y:2014:i:c:p:172-185
    DOI: 10.1016/j.eneco.2014.06.014
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    References listed on IDEAS

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    1. Li, Minqiang, 2008. "Closed-Form Approximations for Spread Option Prices and Greeks," MPRA Paper 6994, University Library of Munich, Germany.
    2. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    3. 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.
    4. Fengler, Matthias R. & Schwendner, Peter, 2003. "Correlation Risk Premia for Multi-Asset Equity Options," SFB 373 Discussion Papers 2003,10, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. 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. Nicola Cufaro Petroni & Piergiacomo Sabino, 2015. "Cointegrating Jumps: an Application to Energy Facilities," Papers 1509.01144, arXiv.org, revised Jul 2016.
    2. Matteo Gardini & Piergiacomo Sabino, 2022. "Exchange option pricing under variance gamma-like models," Papers 2207.00453, arXiv.org.

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    More about this item

    Keywords

    Energy Derivatives; Spread Options; Moment-Matching; Energy Assets and Computational Finance;
    All these keywords.

    JEL classification:

    • O13 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Agriculture; Natural Resources; Environment; Other Primary Products
    • Q4 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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