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Calibration of Local-Stochastic and Path-Dependent Volatility Models to Vanilla and No-Touch Options

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  • Alan Bain
  • Matthieu Mariapragassam
  • Christoph Reisinger

Abstract

We propose a generic calibration framework to both vanilla and no-touch options for a large class of continuous semi-martingale models. The method builds upon the forward partial integro-differential equation (PIDE) derived in Hambly et al. (2016), which allows fast computation of up-and-out call prices for the complete set of strikes, barriers and maturities. It also utilises a novel two-states particle method to estimate the Markovian projection of the variance onto the spot and running maximum. We detail a step-by-step procedure for a Heston-type local-stochastic volatility model with local vol-of-vol, as well as two path-dependent volatility models where the local volatility component depends on the running maximum. In numerical tests, we benchmark these new models against standard models for a set of EURUSD market data, all three models are seen to calibrate well within the market no-touch bid--ask.

Suggested Citation

  • Alan Bain & Matthieu Mariapragassam & Christoph Reisinger, 2019. "Calibration of Local-Stochastic and Path-Dependent Volatility Models to Vanilla and No-Touch Options," Papers 1911.00877, arXiv.org.
    • Handle: RePEc:arx:papers:1911.00877
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Florence Guillaume & Wim Schoutens, 2014. "Heston Model: The Variance Swap Calibration," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 76-89, April.
    3. Peter Carr & John Crosby, 2010. "A class of Levy process models with almost exact calibration to both barrier and vanilla FX options," Quantitative Finance, Taylor & Francis Journals, vol. 10(10), pages 1115-1136.
    4. Ben Hambly & Matthieu Mariapragassam & Christoph Reisinger, 2016. "A forward equation for barrier options under the Brunick & Shreve Markovian projection," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 827-838, June.
    5. René Carmona & Sergey Nadtochiy, 2009. "Local volatility dynamic models," Finance and Stochastics, Springer, vol. 13(1), pages 1-48, January.
    6. Ben Hambly & Matthieu Mariapragassam & Christoph Reisinger, 2014. "A Forward Equation for Barrier Options under the Brunick&Shreve Markovian Projection," Papers 1411.3618, arXiv.org, revised Sep 2016.
    7. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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