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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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    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    8. Pagliarani, Stefano & Pascucci, Andrea, 2011. "Analytical approximation of the transition density in a local volatility model," MPRA Paper 31107, University Library of Munich, Germany.
    9. David S. Bates, "undated". "The Cash Premium: Option Pricing Under Asymmetric Processes, with Applications to Options on Deutschemark Futures," Rodney L. White Center for Financial Research Working Papers 36-88, Wharton School Rodney L. White Center for Financial Research.
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    Cited by:

    1. P. Carr & A. Itkin & D. Muravey, 2022. "Semi-analytical pricing of barrier options in the time-dependent Heston model," Papers 2202.06177, arXiv.org.
    2. Andrey Itkin & Dmitry Muravey, 2021. "Semi-analytical pricing of barrier options in the time-dependent $\lambda$-SABR model," Papers 2109.02134, arXiv.org.
    3. Julio Guerrero & Giuseppe Orlando, 2022. "Stochastic Local Volatility models and the Wei-Norman factorization method," Papers 2201.11241, arXiv.org.

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