MOMENT EXPLOSIONS AND LONG‐TERM BEHAVIOR OF AFFINE STOCHASTIC VOLATILITY MODELS
By Martin Keller‐Ressel. 2008
123 citations recorded by the source corpus.
We consider a class of asset pricing models, where the risk‐neutral joint process of log‐price and its stochastic variance is an affine process in the sense of Duffie, Filipovic, and Schachermayer. First we obtain conditions for the price process to be conservative and a martingale. Then we present some results on the long‐term behavior of the model, including an expression for the invariant distribution of the stochastic variance process. We study moment explosions of the price process, and provide explicit expressions for the time at which a moment of given order becomes infinite. We discuss applications of these results, in particular to the asymptotics of the implied volatility smile, and conclude with some calculations for the Heston model, a model of Bates and the Barndorff‐Nielsen–Shephard model.
Subfields: Demography, Finance
View Paper: https://www.semanticscholar.org/paper/fb73a3317c10023110a668e1a06fe2e4229fba51
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In Demography
- Eberhard Mayerhofer
- Damir Filipovi'c
- Michael Tehranchi
- Martin Forde
- Antoine Jacquier
- Martin Keller‐Ressel
- Walter Schachermayer
In Finance
- Eberhard Mayerhofer
- Martin Keller‐Ressel
- Damir Filipovi'c
- Josef Teichmann
- Antoine Jacquier
- Michael Tehranchi
- Martin Forde
- Walter Schachermayer
Citations in the corpus
- Affine Diffusion Processes: Theory and Applications (2009, methodology): “We mention here explicitly just the few articles [2, 4, 8, 10, 13, 14, 16, 20, 26 , 27, 29] and [12] for a broader overview.”
- Affine processes are regular (2009, background): “Note that semi-homogeneous affine processes are frequently encountered in mathematical finance: Affine stochastic volatility models (e.g. the Heston model) are typically based on a semi-homogeneous affine process; see Keller-Ressel (2008a).”
- Exponential moments of affine processes (2011, background): “It is well understood that the existence of moments E[Syt ] with y ∈ R is intimately connected to the shape of the implied volatility surface derived from the prices of options on the underlying S; cf. Lee (2004), Keller-Ressel (2011).”
- SMALL-TIME ASYMPTOTICS FOR IMPLIED VOLATILITY UNDER THE HESTON MODEL (2009, background): “1, part (iii) in Andersen and Piterbarg [3], see also Keller-Ressel [17]).”
- Asymptotics of Implied Volatility far from Maturity (2009, background): “Following Keller-Ressel’s paper [8], we note that when (prζ − λ)2 > ζ 2p(p − 1), the Riccati equation has two fixed points, A−(p) < A+(p), with A−(p) stable and A+(p) unstable.”
- Asymptotic formulae for implied volatility in the Heston model (2009, unknown): “Recall that [12], [29], and [22] have already derived the leading order term for the implied volatility in the large-time, fixed-strike case.”