Moment explosions in stochastic volatility models

By Leif Andersen, Vladimir V. Piterbarg. Finance and Stochastics, 2006

400 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/eb9f44bca4955f62c8726a2a5bd45ad2ffbe872b

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Citations in the corpus

Fast strong approximation Monte Carlo schemes for stochastic volatility models (2006, methodology): “The stationary distribution of this process can be calculated as (see Andersen and Piterbarg ( 2004 , Prop.”
The Black–Scholes equation in stochastic volatility models (2010, background): “In fact, higher moments do not exist in general for these models, see [1], so superlinear contracts may have infinite prices.”
Asymptotic Behavior of the Stock Price Distribution Density and Implied Volatility in Stochastic Volatility Models (2009, neutral): “The next result was obtained in [1].”
EXPLICIT IMPLIED VOLATILITIES FOR MULTIFACTOR LOCAL‐STOCHASTIC VOLATILITY MODELS (2013, neutral): “In the Heston model, the dynamics of the underlying S are given by As pointed out in Andersen and Piterbarg (2007), one must set ρ 0 in order to prevent a moment explosion.”
COMPLEX LOGARITHMS IN HESTON‐LIKE MODELS (2010, methodology): “To this end it is convenient to use the critical time analysed in Andersen and Piterbarg [2007]. In Lord and Kahl [2007] good starting solutions are provided.”
A LOW-BIAS SIMULATION SCHEME FOR THE SABR STOCHASTIC VOLATILITY MODEL (2012, background): “It was argued by Andersen [4] that the continuous time process, St, will be a martingale with E[St+∆|St] = St < ∞.”
Affine Diffusion Processes: Theory and Applications (2009, background): “We mention here explicitly just the few articles [2, 4, 8, 10, 13, 14, 17, 21, 26, 27, 29] and [12] for a broader overview.”
Asymptotic formulae for implied volatility in the Heston model (2009, neutral): “1 Introduction The Heston model introduced in 1993, [19], has become one of the most widely used stochastic volatility models in the derivatives market (see [14], [29], [2], [3], [28]).”
A comparison of biased simulation schemes for stochastic volatility models (2010, background): “Andersen and Brotherton-Ratcliffe ( 2005 ) and Andersen and Piterbarg ( 2007 ).”
Option pricing under hybrid stochastic and local volatility (2013, background): “If ρ > 0, then Xt may fail to be a true martingale because Yt may explode to infinity under the risk-neutral measure (Andersen and Piterbarg 2007).”
Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients (2013, methodology): “We refer the reader to Andersen and Piterbarg [3] for a good overview of this topic.”
MOMENT EXPLOSIONS AND LONG‐TERM BEHAVIOR OF AFFINE STOCHASTIC VOLATILITY MODELS (2008, methodology): “As mentioned above, moment explosions in the Heston model (and other models) have already been studied by Andersen and Piterbarg [2007]. Nevertheless this will provide a first test of Theorem 4.”
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]).”
MOMENT EXPLOSIONS AND STATIONARY DISTRIBUTIONS IN AFFINE DIFFUSION MODELS (2010, methodology): “Stochastic Volatility: A Simple Case To illustrate our results, we begin by considering the stochastic volatility model (2.3)– (2.5), based on the A1(2) dynamics in (2.3)–(2.4).”
Perfect hedging in rough Heston models (2017, neutral): “Moreover the set of a ∈ R such that λ− ρνa > 0, a− ≤ a ≤ a+, exactly corresponds to that of a ∈ R for which ∀t ≥ 0, E[(St)] <∞, see [2] for further details on moment explosions for the classical Heston model.”
SMILE ASYMPTOTICS II: MODELS WITH KNOWN MOMENT GENERATING FUNCTIONS (2006, background): “Hence, the distribution function for the Heston returns satisfies log Fix) ~ ?px, where p is solution to (see [2])”