TY - JOUR
T1 - Financial market models with Lévy processes and time-varying volatility
AU - Kim, Young Shin
AU - Rachev, Svetlozar T.
AU - Bianchi, Michele Leonardo
AU - Fabozzi, Frank J.
N1 - Funding Information:
This paper was reviewed and accepted while Prof. Giorgio Szegö was the Managing Editor of The Journal of Banking and Finance and by the past Editorial Board. Rachev’s research was supported by Grants from the Division of Mathematical, Life and Physical Science, College of Letters and Science, University of California, Santa Barbara, and the Deutsche Forschungsgemeinschaft. Bianchi is grateful for research support provided by the German Academic Exchange Service (DAAD).
PY - 2008/7
Y1 - 2008/7
N2 - Asset management and pricing models require the proper modeling of the return distribution of financial assets. While the return distribution used in the traditional theories of asset pricing and portfolio selection is the normal distribution, numerous studies that have investigated the empirical behavior of asset returns in financial markets throughout the world reject the hypothesis that asset return distributions are normally distribution. Alternative models for describing return distributions have been proposed since the 1960s, with the strongest empirical and theoretical support being provided for the family of stable distributions (with the normal distribution being a special case of this distribution). Since the turn of the century, specific forms of the stable distribution have been proposed and tested that better fit the observed behavior of historical return distributions. More specifically, subclasses of the tempered stable distribution have been proposed. In this paper, we propose one such subclass of the tempered stable distribution which we refer to as the "KR distribution". We empirically test this distribution as well as two other recently proposed subclasses of the tempered stable distribution: the Carr-Geman-Madan-Yor (CGMY) distribution and the modified tempered stable (MTS) distribution. The advantage of the KR distribution over the other two distributions is that it has more flexible tail parameters. For these three subclasses of the tempered stable distribution, which are infinitely divisible and have exponential moments for some neighborhood of zero, we generate the exponential Lévy market models induced from them. We then construct a new GARCH model with the infinitely divisible distributed innovation and three subclasses of that GARCH model that incorporates three observed properties of asset returns: volatility clustering, fat tails, and skewness. We formulate the algorithm to find the risk-neutral return processes for those GARCH models using the "change of measure" for the tempered stable distributions. To compare the performance of those exponential Lévy models and the GARCH models, we report the results of the parameters estimated for the S&P 500 index and investigate the out-of-sample forecasting performance for those GARCH models for the S&P 500 option prices.
AB - Asset management and pricing models require the proper modeling of the return distribution of financial assets. While the return distribution used in the traditional theories of asset pricing and portfolio selection is the normal distribution, numerous studies that have investigated the empirical behavior of asset returns in financial markets throughout the world reject the hypothesis that asset return distributions are normally distribution. Alternative models for describing return distributions have been proposed since the 1960s, with the strongest empirical and theoretical support being provided for the family of stable distributions (with the normal distribution being a special case of this distribution). Since the turn of the century, specific forms of the stable distribution have been proposed and tested that better fit the observed behavior of historical return distributions. More specifically, subclasses of the tempered stable distribution have been proposed. In this paper, we propose one such subclass of the tempered stable distribution which we refer to as the "KR distribution". We empirically test this distribution as well as two other recently proposed subclasses of the tempered stable distribution: the Carr-Geman-Madan-Yor (CGMY) distribution and the modified tempered stable (MTS) distribution. The advantage of the KR distribution over the other two distributions is that it has more flexible tail parameters. For these three subclasses of the tempered stable distribution, which are infinitely divisible and have exponential moments for some neighborhood of zero, we generate the exponential Lévy market models induced from them. We then construct a new GARCH model with the infinitely divisible distributed innovation and three subclasses of that GARCH model that incorporates three observed properties of asset returns: volatility clustering, fat tails, and skewness. We formulate the algorithm to find the risk-neutral return processes for those GARCH models using the "change of measure" for the tempered stable distributions. To compare the performance of those exponential Lévy models and the GARCH models, we report the results of the parameters estimated for the S&P 500 index and investigate the out-of-sample forecasting performance for those GARCH models for the S&P 500 option prices.
KW - G12
KW - G20
KW - GARCH model
KW - Option pricing
KW - Tempered stable distribution
UR - http://www.scopus.com/inward/record.url?scp=43949126870&partnerID=8YFLogxK
U2 - 10.1016/j.jbankfin.2007.11.004
DO - 10.1016/j.jbankfin.2007.11.004
M3 - Article
AN - SCOPUS:43949126870
SN - 0378-4266
VL - 32
SP - 1363
EP - 1378
JO - Journal of Banking and Finance
JF - Journal of Banking and Finance
IS - 7
ER -