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Fixed-point iterative algorithm for SVI model

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  • Shuzhen Yang
  • Wenqing Zhang

Abstract

The stochastic volatility inspired (SVI) model is widely used to fit the implied variance smile. Presently, most optimizer algorithms for the SVI model have a strong dependence on the input starting point. In this study, we develop an efficient iterative algorithm for the SVI model based on a fixed-point and least-square optimizer. Furthermore, we present the convergence results in certain situations for this novel iterative algorithm. Compared with the quasi-explicit SVI method, we demonstrate the advantages of the fixed-point iterative algorithm using simulation and market data.

Suggested Citation

  • Shuzhen Yang & Wenqing Zhang, 2023. "Fixed-point iterative algorithm for SVI model," Papers 2301.07830, arXiv.org.
    • Handle: RePEc:arx:papers:2301.07830
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    References listed on IDEAS

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    1. Jim Gatheral & Antoine Jacquier, 2014. "Arbitrage-free SVI volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 59-71, January.
    2. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
    3. Martin Forde & Antoine Jacquier & Aleksandar Mijatovic, 2009. "Asymptotic formulae for implied volatility in the Heston model," Papers 0911.2992, arXiv.org, revised May 2010.
    4. Yacine Aït-Sahalia & Chenxu Li & Chen Xu Li, 2021. "Implied Stochastic Volatility Models [Testing continuous-time models of the spot interest rate]," The Review of Financial Studies, Society for Financial Studies, vol. 34(1), pages 394-450.
    5. Jim Gatheral & Antoine Jacquier, 2011. "Convergence of Heston to SVI," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1129-1132.
    6. Yacine Aït-Sahalia & Chenxu Li & Chen Xu Li & Ralph Koijen, 2021. "Implied Stochastic Volatility Models," Review of Economic Studies, Oxford University Press, vol. 34(1), pages 394-450.
    7. Arianna Mingone, 2022. "No arbitrage global parametrization for the eSSVI volatility surface," Papers 2204.00312, arXiv.org.
    8. A. Mingone, 2022. "No arbitrage global parametrization for the eSSVI volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 22(12), pages 2205-2217, December.
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