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Approximate pricing of European and Barrier claims in a local-stochastic volatility setting

Author

Listed:
  • Weston Barger

    (Department of Applied Mathematics, University of Washington, USA)

  • Matthew Lorig

    (Department of Applied Mathematics, University of Washington, USA)

Abstract

We derive asymptotic expansions for the prices of a variety of European and barrier-style claims in a general local-stochastic volatility setting. Our method combines Taylor series expansions of the diffusion coefficients with an expansion in the correlation parameter between the underlying asset and volatility process. Rigorous accuracy results are provided for European-style claims. For barrier-style claims, we include several numerical examples to illustrate the accuracy and versatility of our approximations.

Suggested Citation

  • Weston Barger & Matthew Lorig, 2017. "Approximate pricing of European and Barrier claims in a local-stochastic volatility setting," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-31, June.
    • Handle: RePEc:wsi:ijfexx:v:04:y:2017:i:02n03:n:s2424786317500189
    DOI: 10.1142/S2424786317500189
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    References listed on IDEAS

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    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
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    5. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2017. "Explicit Implied Volatilities For Multifactor Local-Stochastic Volatility Models," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 926-960, July.
    6. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "Analytical expansions for parabolic equations," Papers 1312.3314, arXiv.org, revised Nov 2014.
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    Cited by:

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    3. Andrey Itkin & Dmitry Muravey, 2021. "Semi-analytical pricing of barrier options in the time-dependent $\lambda$-SABR model," Papers 2109.02134, arXiv.org.

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