TY - JOUR
T1 - Calibrating the Italian Smile with Time-Varying Volatility and Heavy-Tailed Models
AU - Bianchi, Michele Leonardo
AU - Rachev, Svetlozar T.
AU - Fabozzi, Frank J.
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2018/3/1
Y1 - 2018/3/1
N2 - 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.
AB - 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.
KW - GARCH model
KW - Lévy processes
KW - Non-Gaussian Ornstein-Uhlenbeck processes
KW - Stochastic volatility models
KW - Tempered stable processes and distributions
KW - Volatility smile
UR - http://www.scopus.com/inward/record.url?scp=84976272662&partnerID=8YFLogxK
U2 - 10.1007/s10614-016-9599-7
DO - 10.1007/s10614-016-9599-7
M3 - Article
AN - SCOPUS:84976272662
SN - 0927-7099
VL - 51
SP - 339
EP - 378
JO - Computational Economics
JF - Computational Economics
IS - 3
ER -