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Calibrating the Italian smile with time-varying volatility and heavy-tailed models


  • Michele Leonardo Bianchi

    () (Bank of Italy)

  • Frank J. Fabozzi

    () (EDHEC Business School)

  • Svetlozar T. Rachev

    () (Stony Brook University)


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 �Borsa Italiana� 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 ten 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 U.S.) 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.

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  • Michele Leonardo Bianchi & Frank J. Fabozzi & Svetlozar T. Rachev, 2014. "Calibrating the Italian smile with time-varying volatility and heavy-tailed models," Temi di discussione (Economic working papers) 944, Bank of Italy, Economic Research and International Relations Area.
  • Handle: RePEc:bdi:wptemi:td_944_14

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    References listed on IDEAS

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    1. repec:wsi:ijtafx:v:17:y:2014:i:04:n:s021902491450023x is not listed on IDEAS
    2. 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.

    More about this item


    volatility smile; option pricing; non-Gaussian Ornstein-Uhlenbeck processes; L�vy processes; tempered stable processes and distributions; stochastic volatility models; time-changed L�vy processes; GARCH model; filtered historical simulation; particle filter;

    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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