TY - GEN
T1 - A new tempered stable distribution and its application to finance
AU - Kim, Young Shin
AU - Rachev, Svetlozar T.
AU - Bianchi, Michele Leonardo
AU - Fabozzi, Frank J.
PY - 2009
Y1 - 2009
N2 - In this paper, we will discuss a parametric approach to risk-neutral density extraction from option prices based on the knowledge of the estimated historical density. A flexible distribution is needed in order to find an equivalent change of measure and, at the same time, take into account the historical estimates. To this end, we introduce a new tempered stable distribution that we refer to as the KR distribution. Some properties of this distribution will be discussed in this paper, along with the advantages in applying it to financial modeling. Since the KR distribution is infinitely divisible, a Lélvy process can be induced from it. Furthermore, we can develop an exponential Lévy model, called the exponential KR model, and prove that it is an extension of the Carr, Geman, Madan, and Yor (CGMY) model. The risk-neutral process is fitted by matching model prices to market prices of options using nonlinear least squares. The easy form of the characteristic function of the KR distribution allows one to obtain a suitable solution to the calibration problem. To demonstrate the advantages of the exponential KR model, we present the results of the parameter estimation for the S&P 500 Index and option prices.
AB - In this paper, we will discuss a parametric approach to risk-neutral density extraction from option prices based on the knowledge of the estimated historical density. A flexible distribution is needed in order to find an equivalent change of measure and, at the same time, take into account the historical estimates. To this end, we introduce a new tempered stable distribution that we refer to as the KR distribution. Some properties of this distribution will be discussed in this paper, along with the advantages in applying it to financial modeling. Since the KR distribution is infinitely divisible, a Lélvy process can be induced from it. Furthermore, we can develop an exponential Lévy model, called the exponential KR model, and prove that it is an extension of the Carr, Geman, Madan, and Yor (CGMY) model. The risk-neutral process is fitted by matching model prices to market prices of options using nonlinear least squares. The easy form of the characteristic function of the KR distribution allows one to obtain a suitable solution to the calibration problem. To demonstrate the advantages of the exponential KR model, we present the results of the parameter estimation for the S&P 500 Index and option prices.
UR - http://www.scopus.com/inward/record.url?scp=77950467480&partnerID=8YFLogxK
U2 - 10.1007/978-3-7908-2050-8-5
DO - 10.1007/978-3-7908-2050-8-5
M3 - Conference contribution
AN - SCOPUS:77950467480
SN - 9783790820492
T3 - Contributions to Economics
SP - 77
EP - 109
BT - Risk Assessment
A2 - Bol, Georg
A2 - Rachev, Svetlozar
A2 - Wurth, Reinhold
ER -