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Quantization goes Polynomial

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  • Giorgia Callegaro
  • Lucio Fiorin
  • Andrea Pallavicini

Abstract

Quantization algorithms have been successfully adopted to option pricing in finance thanks to the high convergence rate of the numerical approximation. In particular, very recently, recursive marginal quantization has been proven to be a flexible and versatile tool when applied to stochastic volatility processes. In this paper we apply for the first time quantization techniques to the family of polynomial processes, by exploiting their peculiar nature. We focus our analysis on the stochastic volatility Jacobi process, by presenting two alternative quantization procedures: the first is a new discretization technique, whose foundation lies on the polynomial structure of the underlying process and which is suitable for vanilla option pricing, the second is based on recursive marginal quantization and it allows for pricing of (vanilla and) exotic derivatives. We prove theoretical results to assess the induced approximation errors, and we describe in numerical examples practical tools for fast vanilla and exotic option pricing.

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  • Giorgia Callegaro & Lucio Fiorin & Andrea Pallavicini, 2017. "Quantization goes Polynomial," Papers 1710.11435, arXiv.org, revised Dec 2019.
    • Handle: RePEc:arx:papers:1710.11435
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    References listed on IDEAS

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    1. T. A. McWalter & R. Rudd & J. Kienitz & E. Platen, 2018. "Recursive marginal quantization of higher-order schemes," Quantitative Finance, Taylor & Francis Journals, vol. 18(4), pages 693-706, April.
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    3. Christa Cuchiero & Martin Keller-Ressel & Josef Teichmann, 2012. "Polynomial processes and their applications to mathematical finance," Finance and Stochastics, Springer, vol. 16(4), pages 711-740, October.
    4. Gilles Pagès & Abass Sagna, 2015. "Recursive Marginal Quantization of the Euler Scheme of a Diffusion Process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(5), pages 463-498, November.
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    6. Vlad Bally & Gilles Pagès & Jacques Printems, 2005. "A Quantization Tree Method For Pricing And Hedging Multidimensional American Options," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 119-168, January.
    7. Damir Filipović & Martin Larsson, 2016. "Polynomial diffusions and applications in finance," Finance and Stochastics, Springer, vol. 20(4), pages 931-972, October.
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