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Calibrating the Italian Smile with Time-Varying Volatility and Heavy-Tailed Models

Author

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  • Michele Leonardo Bianchi

    (Bank of Italy)

  • Svetlozar T. Rachev

    (Stony Brook University)

  • Frank J. Fabozzi

    (EDHEC Business School)

Abstract

In this paper, we consider several time-varying volatility and/or heavy-tailed models to explain the dynamics of return time series and to fit the volatility smile for exchange-traded options where the underlying is the main Italian stock index. Given observed prices for the time period we investigate, we calibrate both continuous-time and discrete-time models. First, we estimate the models from a time-series perspective (i.e. under the historical probability measure) by investigating more than 10 years of daily index price log-returns. Then, we explore the risk-neutral measure by fitting the values of the implied volatility for numerous strikes and maturities during the highly volatile period from April 1, 2007 (prior to the subprime mortgage crisis in the US) to March 30, 2012. We assess the extent to which time-varying volatility and heavy-tailed distributions are needed to explain the behavior of the most important stock index of the Italian market.

Suggested Citation

  • Michele Leonardo Bianchi & Svetlozar T. Rachev & Frank J. Fabozzi, 2018. "Calibrating the Italian Smile with Time-Varying Volatility and Heavy-Tailed Models," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 339-378, March.
    • Handle: RePEc:kap:compec:v:51:y:2018:i:3:d:10.1007_s10614-016-9599-7
    DOI: 10.1007/s10614-016-9599-7
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    Cited by:

    1. Gian Luca Tassinari & Michele Leonardo Bianchi, 2014. "Calibrating The Smile With Multivariate Time-Changed Brownian Motion And The Esscher Transform," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-34.
    2. Kim, Sangkwon & Kim, Junseok, 2021. "Robust and accurate construction of the local volatility surface using the Black–Scholes equation," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Michele Leonardo Bianchi & Gian Luca Tassinari, 2018. "Forward-looking portfolio selection with multivariate non-Gaussian models and the Esscher transform," Papers 1805.05584, arXiv.org, revised May 2018.
    4. Michele Bianchi & Frank Fabozzi, 2014. "Discussion of ‘on simulation and properties of the stable law’ by Devroye and James," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 353-357, August.

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    More about this item

    Keywords

    Volatility smile; Stochastic volatility models; GARCH model; Non-Gaussian Ornstein-Uhlenbeck processes; Lévy processes; Tempered stable processes and distributions;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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