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Consistent Recalibration Models and Deep Calibration

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  • Matteo Gambara
  • Josef Teichmann

Abstract

Consistent Recalibration models (CRC) have been introduced to capture in necessary generality the dynamic features of term structures of derivatives' prices. Several approaches have been suggested to tackle this problem, but all of them, including CRC models, suffered from numerical intractabilities mainly due to the presence of complicated drift terms or consistency conditions. We overcome this problem by machine learning techniques, which allow to store the crucial drift term's information in neural network type functions. This yields first time dynamic term structure models which can be efficiently simulated.

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  • Matteo Gambara & Josef Teichmann, 2020. "Consistent Recalibration Models and Deep Calibration," Papers 2006.09455, arXiv.org, revised Jul 2021.
    • Handle: RePEc:arx:papers:2006.09455
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    References listed on IDEAS

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    1. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    2. Christa Cuchiero & Josef Teichmann, 2011. "Path properties and regularity of affine processes on general state spaces," Papers 1107.1607, arXiv.org, revised Jan 2013.
    3. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A Generative Adversarial Network Approach to Calibration of Local Stochastic Volatility Models," Risks, MDPI, vol. 8(4), pages 1-31, September.
    4. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    5. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A generative adversarial network approach to calibration of local stochastic volatility models," Papers 2005.02505, arXiv.org, revised Sep 2020.
    6. Martin Schweizer & Johannes Wissel, 2008. "Term Structures Of Implied Volatilities: Absence Of Arbitrage And Existence Results," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 77-114, January.
    7. Yuri F. Saporito & Xu Yang & Jorge P. Zubelli, 2017. "The Calibration of Stochastic-Local Volatility Models - An Inverse Problem Perspective," Papers 1711.03023, arXiv.org.
    8. Philipp Harms & David Stefanovits & Josef Teichmann & Mario V. Wüthrich, 2018. "Consistent recalibration of yield curve models," Mathematical Finance, Wiley Blackwell, vol. 28(3), pages 757-799, July.
    9. Blanka Horvath & Aitor Muguruza & Mehdi Tomas, 2019. "Deep Learning Volatility," Papers 1901.09647, arXiv.org, revised Aug 2019.
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