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Computational Economics

, Volume 51, Issue 3, pp 339–378 | Cite as

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

  • Michele Leonardo Bianchi
  • Svetlozar T. Rachev
  • Frank J. FabozziEmail author
Article

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.

Keywords

Volatility smile Stochastic volatility models GARCH model Non-Gaussian Ornstein-Uhlenbeck processes Lévy processes Tempered stable processes and distributions 

Mathematics Subject Classification

60E07 60G51 91G20 91G60 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Michele Leonardo Bianchi
    • 1
  • Svetlozar T. Rachev
    • 2
  • Frank J. Fabozzi
    • 3
    Email author
  1. 1.Regulation and Macroprudential Analysis DirectorateBank of ItalyRomeItaly
  2. 2.Department of Applied Mathematics and Statistics, College of BusinessStony Brook UniversityNew YorkUSA
  3. 3.EDHEC Business SchoolNiceFrance

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