Calibrating the Italian smile with time-varying volatility and heavy-tailed models
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 ï¿½Borsa Italianaï¿½ 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.
|Date of creation:||Jan 2014|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.bancaditalia.it
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- Shin Kim, Young & Rachev, Svetlozar T. & Leonardo Bianchi, Michele & Fabozzi, Frank J., 2010.
"Tempered stable and tempered infinitely divisible GARCH models,"
Journal of Banking & Finance,
Elsevier, vol. 34(9), pages 2096-2109, September.
- Kim, Young Shin & Rachev, Svetlozar T. & Bianchi, Michele Leonardo & Fabozzi, Frank J., 2011. "Tempered stable and tempered infinitely divisible GARCH models," Working Paper Series in Economics 28, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
- Silvia Muzzioli, 2011. "Corridor implied volatility and the variance risk premium in the Italian market," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 11112, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
- Simon Hurst & Eckhard Platen & Svetlozar Rachev, 1997. "Subordinated Market Index Models: A Comparison," Asia-Pacific Financial Markets, Springer, vol. 4(2), pages 97-124, May.
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
- Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO.
- Jin-Chuan Duan & Jean-Guy Simonato, 1998. "Empirical Martingale Simulation for Asset Prices," Management Science, INFORMS, vol. 44(9), pages 1218-1233, September.
- Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
- Li, Junye, 2011. "Sequential Bayesian Analysis of Time-Changed Infinite Activity Derivatives Pricing Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 468-480.
- Giovanni Barone-Adesi & Robert F. Engle & Loriano Mancini, 2008. "A GARCH Option Pricing Model with Filtered Historical Simulation," Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1223-1258, May.
- Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
- Lehar, Alfred & Scheicher, Martin & Schittenkopf, Christian, 2002. "GARCH vs. stochastic volatility: Option pricing and risk management," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 323-345, March.
- Florence Guillaume & Wim Schoutens, 2012. "Calibration risk: Illustrating the impact of calibration risk under the Heston model," Review of Derivatives Research, Springer, vol. 15(1), pages 57-79, April.
- Peter Christoffersen & Kris Jacobs & Karim Mimouni, 2010. "Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns, and Option Prices," Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3141-3189, August.
- Marc Yor & Dilip B. Madan & Hélyette Geman, 2002. "Stochastic volatility, jumps and hidden time changes," Finance and Stochastics, Springer, vol. 6(1), pages 63-90.
- Matthias Scherer & Svetlozar T. Rachev & Young Shin Kim & Frank J. Fabozzi, 2012. "Approximation of skewed and leptokurtic return distributions," Applied Financial Economics, Taylor & Francis Journals, vol. 22(16), pages 1305-1316, August.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
- Engle, Robert F & Ng, Victor K, 1993.
" Measuring and Testing the Impact of News on Volatility,"
Journal of Finance,
American Finance Association, vol. 48(5), pages 1749-78, December.
- Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
When requesting a correction, please mention this item's handle: RePEc:bdi:wptemi:td_944_14. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.