Modelling by L´ evy Processes for Financial Econometrics

By Ole E. Barndorff-Nielsen, N. Shephard. 2000

261 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3935d61dd196eed6c49a4446aa21625f1e5771bb

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Citations in the corpus

The Meixner process : theory and applications in finance (2002, background): “A number of stylized features of observational series from finance are discussed in [3].”
A continuous-time GARCH process driven by a Lévy process: stationarity and second-order behaviour (2004, methodology): “In this paper, as well as in [2, 3], the logarithmic price process is modelled by the SDE dx∗(t) = (μ+ bσ(t))dt+ σ(t)dW (t) , t > 0 , where μ and b are constants and (W (t))t≥0 is standard Brownian motion, independent of the Lévy process (Lt)t≥0.”
Ornstein–Uhlenbeck Processes and Extensions (2009, background): “…motivation for studying (12) is that special cases of it occupy central positions in certain models of financial time series; the Lévy driven OU processes of Barndorff-Nielsen and Shephard (2001a, 2001b, 2003) and the COGARCH process of Klüppelberg, Lindner and Maller (2004) are recent examples.”
Valuing path dependent options in the variance-gamma model by Monte Carlo with a gamma bridge (2002, background): “Following Madan, Carr and Chang (98) [14], Barndorff-Nielsen and Shephard (00) [5], Eberlein and Keller (95) [12], et cetera, we model a stock price process St under the pricing measure2 F as St = S0 exp (rt+Xt −$t) (7)”
Affine Processes on Positive Semidefinite Matrices (2009, unknown): “3This affine multi-variate stochastic volatility model generalizes the well-known one-dimensional models of Heston [27], for the diffusion case, or the Barndorff-Nielsen Shepard model [2], for the pure jump case.”
Extremal behavior of stochastic volatility models (2006, methodology): “Hence L is a positive compound Poisson process with Poisson rate µ > 0 and exponential jumps; for details see Barndorff-Nielsen and Shephard [2].”
Nonparametric Risk Management With Generalized Hyperbolic Distributions (2005, unknown): “…feature of financial risk factors, various heavy-tailed distribution families, such as the hyperbolic and Student t distributions and the Lévy process, have been introduced in finance by Eberlein and Keller (1995), Embrechts, McNeil, and Straumann (1999), and Barndorff-Nielsen and Shephard (2001).”
Self-decomposability and Lévy processes in free probability (2002, background): “Applications of self-decomposability are discussed, inter alia, in Brockwell et al. (1982), Barndorff-Nielsen (1998) and Barndorff- Nielsen and Shephard (2001a; 2001b).”
Normal Modified Stable Processes (2001, methodology): “An important relationship between these two functions is that (cf. Barndorff-Nielsen and Shephard (2001b)) k(θ) = θḱ′(θ).”
Simulation Methods for Lévy-Driven Continuous-Time Autoregressive Moving Average (CARMA) Stochastic Volatility Models (2006, methodology): “This is an example of a completely dependent Lévy process, such as those used by Barndorff-Nielsen and Shephard (2001b) or Carr and Wu (2004), among others.”