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A First Option Calibration of the GARCH Diffusion Model by a PDE Method

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  • Yiannis A. Papadopoulos
  • Alan L. Lewis

Abstract

Time-series calibrations often suggest that the GARCH diffusion model could also be a suitable candidate for option (risk-neutral) calibration. But unlike the popular Heston model, it lacks a fast, semi-analytic solution for the pricing of vanilla options, perhaps the main reason why it is not used in this way. In this paper we show how an efficient finite difference-based PDE solver can effectively replace analytical solutions, enabling accurate option calibrations in less than a minute. The proposed pricing engine is shown to be robust under a wide range of model parameters and combines smoothly with black-box optimizers. We use this approach to produce a first PDE calibration of the GARCH diffusion model to SPX options and present some benchmark results for future reference.

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  • Yiannis A. Papadopoulos & Alan L. Lewis, 2018. "A First Option Calibration of the GARCH Diffusion Model by a PDE Method," Papers 1801.06141, arXiv.org.
    • Handle: RePEc:arx:papers:1801.06141
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    References listed on IDEAS

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    5. Peter Christoffersen & Kris Jacobs & Karim Mimouni, 2010. "Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns, and Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3141-3189, August.
    6. 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.
    7. Nicolas Langren'e & Geoffrey Lee & Zili Zhu, 2015. "Switching to non-affine stochastic volatility: A closed-form expansion for the Inverse Gamma model," Papers 1507.02847, arXiv.org, revised Mar 2016.
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    Cited by:

    1. Alan L. Lewis, 2018. "Exact Solutions for a GBM-type Stochastic Volatility Model having a Stationary Distribution," Papers 1809.08635, arXiv.org, revised May 2019.

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