Asymptotics and calibration of local volatility models

By H. Berestycki, J. Busca, Igor Florent. 2002

196 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/ce39cfb956af87ad11419a0dfdc4487fc4d732b0

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Citations in the corpus

SMALL-TIME ASYMPTOTICS FOR IMPLIED VOLATILITY UNDER THE HESTON MODEL (2009, background): “[4, 5], Henry-Labordère [14, 15] and Laurence [18].”
Small-Time Asymptotics of Option Prices and First Absolute Moments (2010, background): “Due to their importance for model calibration and testing, small-time asymptotics of option prices have received considerable attention in recent years; see [2, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 22, 24].”
ASYMPTOTICS OF IMPLIED VOLATILITY IN LOCAL VOLATILITY MODELS (2012, methodology): “17) originally derived in [4]: σ0(K, t) = log(s/K) ∫ s K dη a(η t) On page 145 of his book, Henry-Labordère presents an alternative approximation to first order in T − t, matching ours exactly in the time-homogeneous case and differing only slightly in the time-inhomogeneous case.”
A General Asymptotic Implied Volatility for Stochastic Volatility Models (2005, methodology): “This relation between the smile at zero-order and the geodesic distance has already been obtained in [ 4 , 5] and used in [2] to compute an asymptotic smile for an equity basket.”
Implied Volatility: Statics, Dynamics, and Probabilistic Interpretation (2005, background): “Specifically, Berestycki, Busca, and Florent ([7]; BBF henceforth) show that in the short-maturity limit, implied volatility is the harmonic mean of local volatility.”
EXPLICIT IMPLIED VOLATILITIES FOR MULTIFACTOR LOCAL‐STOCHASTIC VOLATILITY MODELS (2013, unknown): “All of our results are consistent with the previously derived short-maturity asymptotic results appearing in Berestycki et al. (2002), Berestycki et al. (2004) and Bompis and Gobet (2012).”
Hermite Polynomial Based Expansion of European Option Prices (2014, unknown): “Most models with closed-form solutions are either confined to the log-normal class (including the famous Black-Scholes-Merton formula by Black and Scholes (1973) and Merton (1976)), or the Bessel process class (e.”
SMALL-TIME ASYMPTOTICS FOR FAST MEAN-REVERTING STOCHASTIC VOLATILITY MODELS (2010, background): “ating function computation in the particular case of the Heston model. 1. Introduction. On one hand, the theory of large deviations has been recently applied to local and stochastic volatility models [1, 2, 4, 5, 20] and has given very interesting results on the behavior of implied volatilities near”
Asymptotic Implied Volatility at the Second Order with Application to the SABR Model (2009, unknown): “h order in T, which gives our nal expansion of the implied volatility. Power 1 gives the order 0 implied volatility ˙ 0 = lnK F 0 ln p 2B = K F 0 d(F 0;V 0;K;V min) (23) which was already obtained in [BBF02] and [HL05]. The rst order correction is extracted from the constant term: ˙ 1 ˙ 0 = Ce+ ln 0”