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Pricing Asian Options In Affine Garch Models

Author

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  • MERCURI LORENZO

    (Dipartimento di Metodi Quantitativi, per le Scienze Economiche ed Aziendali, University of Milano-Bicocca, P.zza Ateneo Nuovo 1, 20126 Milano, Italy)

Abstract

We derive recursive relationships for the m.g.f. of the geometric average of the underlying within some affine Garch models [Heston and Nandi (2000), Christoffersen et al. (2006), Bellini and Mercuri (2007), Mercuri (2008)] and use them for the semi-analytical valuation of geometric Asian options. Similar relationships are obtained for low order moments of the arithmetic average, that are used for an approximated valuation of arithmetic Asian options based on truncated Edgeworth expansions, following the approach of Turnbull and Wakeman (1991). In both cases the accuracy of the semi-analytical procedure is assessed by means of a comparison with Monte Carlo prices. The results are quite good in the geometric case, while in the arithmetic case the proposed methodology seems to work well only in the Heston and Nandi case.

Suggested Citation

  • Mercuri Lorenzo, 2011. "Pricing Asian Options In Affine Garch Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 313-333.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:02:n:s0219024911006371
    DOI: 10.1142/S0219024911006371
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    Cited by:

    1. Gianluca Fusai & Ioannis Kyriakou, 2016. "General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 531-559, May.
    2. Corsaro, Stefania & Kyriakou, Ioannis & Marazzina, Daniele & Marino, Zelda, 2019. "A general framework for pricing Asian options under stochastic volatility on parallel architectures," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1082-1095.

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