Continuous time volatility modelling: COGARCH versus Ornstein-Uhlenbeck models

By Claudia Klüppelberg, A. Lindner, Ross Maller. 2006

83 citations recorded by the source corpus.

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Citations in the corpus

Tail asymptotics for exponential function-als of L evy processes (2006, unknown): “Random variables of this form have recently been analyzed in great detail; the reason being that such random variables appear in several applications, like mathematical finance (Z as the present value of a perpetuity [11], Asian options and COGARCH process [23]), Additive Increase Multiplicative Dec”
Extremes of supOU Processes (2007, unknown): “∗Center for Mathematical Sciences, Munich University of Technology, D-85747 Garching, Ger- many, email: {fasen, cklu}@ma.tum.de, www.ma.tum.de/stat/”
Continuous-time GARCH processes (2006, background): “The Annals of Applied Probability 2006, Vol. 16, No. 2, 790–826 DOI: 10.1214/105051606000000150 © Institute of Mathematical Statistics, 2006”
GARCH modelling in continuous time for irregularly spaced time series data (2008, background): “We refer to [14] and [15] for detailed properties of G and σ(2).”
Multivariate models for operational risk (2010, methodology): “…with an estimate for the second ratio: lemma 1.3.5 of Embrechts et al. (1997) applies, giving for arbitrary "40 and all x40 a finite positive constant K(") so that Pð Pk i¼1 X 1 i 4 xÞ PðX1 4 xÞ Kð"Þð1þ "Þ k: For the first ratio we proceed as in the proof of lemma 2 of Klüppelberg et al. (2005).”
Method of Moment Estimation in the Cogarch(1,1) Model (2007, methodology): “In Klüppelberg et al. (2004, 2006), such a model was suggested by iterating the volatility equation in (1) and replacing the noise variables i by the jumps Lt = Lt − Lt− of a Lévy C© Royal Economic Society 2007.”
Extremal behavior of stochastic volatility models (2006, background): “The stationarity conditions for (Ot)t≥0, along with other properties, have been investigated by Lindner and Maller [30].”
Ornstein–Uhlenbeck Processes and Extensions (2009, methodology): “Further analysis of the COGARCH is in Klüppelberg et al. (2004, 2006), where stationarity properties are related to the convergence of a Lévy integral.”