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Matched asymptotic expansions in financial engineering

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  • Sam Howison

Abstract

Modern financial practice depends heavily on mathematics and a correspondingly large theory has grown up to meet this demand. This paper focuses on the use of matched asymptotic expansions in option pricing; it presents illustrations of the approach in `plain vanilla' option valuation, in valuation using a fast mean-reverting-stochastic volatility model, and in a model for illiquid markets. A tentative framework for matched asymptotic expansions applied directly to stochastic processes of diffusion type is also proposed.

Suggested Citation

  • Sam Howison, 2005. "Matched asymptotic expansions in financial engineering," OFRC Working Papers Series 2005mf01, Oxford Financial Research Centre.
    • Handle: RePEc:sbs:wpsefe:2005mf01
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    File URL: http://www.finance.ox.ac.uk/file_links/finecon_papers/2005mf01.pdf
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    Cited by:

    1. Jean-Pierre Fouque & Matthew Lorig & Ronnie Sircar, 2016. "Second order multiscale stochastic volatility asymptotics: stochastic terminal layer analysis and calibration," Finance and Stochastics, Springer, vol. 20(3), pages 543-588, July.
    2. Sam Howison & Mario Steinberg, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 63-89.
    3. Peter W. Duck & Chao Yang & David P. Newton & Martin Widdicks, 2009. "Singular Perturbation Techniques Applied To Multiasset Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 457-486, July.
    4. Pagliarani, Stefano & Pascucci, Andrea, 2011. "Analytical approximation of the transition density in a local volatility model," MPRA Paper 31107, University Library of Munich, Germany.
    5. Simona Svoboda-Greenwood, 2009. "Displaced Diffusion as an Approximation of the Constant Elasticity of Variance," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 269-286.
    6. He, Xin-Jiang & Zhu, Song-Ping, 2016. "An analytical approximation formula for European option pricing under a new stochastic volatility model with regime-switching," Journal of Economic Dynamics and Control, Elsevier, vol. 71(C), pages 77-85.
    7. Jeff Dewynne & Nadima El-Hassan, 2013. "Self-funding Instalment Warrants," Research Paper Series 339, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Fannu Hu & Charles Knessl, 2010. "Asymptotics of Barrier Option Pricing Under the CEV Process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 261-300.
    9. Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, François, 2008. "Pricing derivatives with barriers in a stochastic interest rate environment," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2903-2938, September.
    10. Stefano, Pagliarani & Pascucci, Andrea & Candia, Riga, 2011. "Expansion formulae for local Lévy models," MPRA Paper 34571, University Library of Munich, Germany.

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