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

54 Pages Posted: 25 Mar 2014

Date Written: January 24, 2014

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 ‘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.

Keywords: volatility smile, option pricing, non-Gaussian Ornstein-Uhlenbeck processes, Lévy processes, tempered stable processes and distributions, stochastic volatility models, time-changed Lévy processes, GARCH model, filtered historical simulation, particle filter

JEL Classification: C02, C46, C58, C61, C63

Suggested Citation

Bianchi, Michele Leonardo and Fabozzi, Frank J. and Rachev, Svetlozar, Calibrating the Italian Smile with Time-Varying Volatility and Heavy-Tailed Models (January 24, 2014). Bank of Italy Temi di Discussione (Working Paper) No. 944, Available at SSRN: https://ssrn.com/abstract=2413459 or http://dx.doi.org/10.2139/ssrn.2413459

Michele Leonardo Bianchi (Contact Author)

Bank of Italy ( email )

Via Nazionale 91
00184 Rome, I - 00184
Italy

Frank J. Fabozzi

EDHEC Business School ( email )

France
215 598-8924 (Phone)

Svetlozar Rachev

Texas Tech University ( email )

Dept of Mathematics and Statistics
Lubbock, TX 79409
United States
631-662-6516 (Phone)

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