Large Deviations for the Extended Heston Model: The Large-Time Case
TLDR
In this article, the large-time behavior of all continuous affine stochastic volatility models (in the sense of Keller-Ressel) and deduce a closed-form formula for the large maturity implied volatility smile was studied.Abstract:
We study here the large-time behavior of all continuous affine stochastic volatility models (in the sense of Keller-Ressel) and deduce a closed-form formula for the large-maturity implied volatility smile. Based on refinements of the Gartner-Ellis theorem on the real line, our proof reveals pathological behaviors of the asymptotic smile. In particular, we show that the condition assumed in Gatheral & Jacquier (GJ10) under which the Heston implied volatility converges to the SVI parameterization is necessary and sufficient.read more
Citations
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Lévy processes and infinitely divisible distributions
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
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Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results
TL;DR: In this paper, the authors study the volatility surface of the Black-Scholes delta and derive numerical methods based on judicial finite-difference approximations for fractional derivatives.
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The large-maturity smile for the SABR and CEV-heston models
Martin Forde,Andrey Pogudin +1 more
TL;DR: In this article, large-time asymptotics are established for the SABR model with β = 1, ρ ≤ 0 and β < 1, ε = 0.
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Large-Maturity Regimes of the Heston Forward Smile
Antoine Jacquier,Patrick Roome +1 more
TL;DR: In this article, a characterisation of the large-maturity forward implied volatility smile in the Heston model is provided, and the proofs are based on extensions and refinements of sharp large deviations theory, particularly in cases where standard convexity arguments fail.
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Amir Dembo,Ofer Zeitouni +1 more
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Lévy processes and infinitely divisible distributions
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
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Moment Explosions in Stochastic Volatility Models
TL;DR: In this paper, the authors demonstrate that many stochastic volatility models have the undesirable property that moments of order higher than one can become infinite in finite time, which is undesirable for the purpose of arbitrage-free price computation for fixed income products.