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

Computational Economics Volume 51, pages 339–378, (2018)

In this article, the authors 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 investigated, they calibrate both continuous-time and discrete-time models. They begin by estimating 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, they 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. They 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, the FTSE MIB index and to properly calibrate the related implied volatility surface.