A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation
Abstract
The purpose of this paper is to propose a new class of jump diffusions which feature
both stochastic volatility and random intensity jumps. Previous studies have focused
primarily on pure jump processes with constant intensity and log-normal jumps or constant
jump intensity combined with a one factor stochastic volatility model. We introduce
several generalizations which can better accommodate several empirical features of
returns data. In their most general form we introduce a class of processes which nests
jump-diffusions previously considered in empirical work and includes the affine class
of random intensity models studied by Bates (1998) and Duffie, Pan and Singleton (1998)
but also allows for non-affine random intensity jump components. We attain the generality
of our specification through a generic Levy process characterization of the jump component.
The processes we introduce share the desirable feature with the affine class that
they yield analytically tractable and explicit option pricing formula. The non-affine
class of processes we study include specifications where the random intensity jump
component depends on the size of the previous jump which represent an alternative
to affine random intensity jump processes which feature correlation between the stochastic
volatility and jump component. We also allow for and experiment with different empirical
specifications of the jump size distributions. We use two types of data sets. One
involves the S&P500 and the other comprises of 100 years of daily Dow Jones index.
The former is a return series often used in the literature and allows us to compare
our results with previous studies. The latter has the advantage to provide a long
time series and enhances the possibility of estimating the jump component more precisely.
The non-affine random intensity jump processes are more parsimonious than the affine
class and appear to fit the data much better.
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https://hdl.handle.net/10161/2028Collections
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Show full item recordScholars@Duke
George E. Tauchen
William Henry Glasson Distinguished Professor Emeritus
George Tauchen is the William Henry Glasson Professor of Economics and professor of
finance at the Fuqua School of Business. He joined the Duke faculty in 1977 after
receiving his Ph.D. from the University of Minnesota. He did his undergraduate work
at the University of Wisconsin. Professor Tauchen is a fellow of the Econometric Society,
the American Statistical Association, the Journal of Econometrics, and the Society
for Financial Econometrics (SoFie). He is also the 2003 Duke University Sc

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