Titlebook: Large Deviations and Asymptotic Methods in Finance; Peter K. Friz,Jim Gatheral,Josef Teichmann Conference proceedings 2015 Springer Intern

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典型

Asymptotic Implied Volatility at the Second Order with Application to the SABR Model,n. Beyond the order 0 implied volatility which is already known, we compute the first order correction exactly at all strikes from the scalar coefficient of the heat kernel expansion. Furthermore, the first correction in the heat kernel expansion gives the second order correction for implied volatil

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Redundant

Second Order Expansion for Implied Volatility in Two Factor Local Stochastic Volatility Models and the short time asymptotics of the local volatility function in a family of time inhomogeneous local-stochastic volatility models. With the local volatility function at our disposal, we show how recent results (Gatheral et al., Math. Financ. 22:591–620, 2012, [.]) for one dimensional diffusions can

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hair-bulb

恶心

Implied Volatility from Local Volatility: A Path Integral Approach,y in terms of a path integral then follows. By Taylor-expanding around a certain path, we obtain a generalization of the heat kernel expansion of the density which coincides with the classical one in the time-homogeneous case, but is more accurate and natural in the time inhomogeneous case. As a fur

habile

,Extrapolation Analytics for Dupire’s Local Volatility,ses our approximation formula from a practical and numerical perspective, the present paper focuses on rigorous proofs of the approximations. We apply the saddle point method (Heston model) and Hankel contour integration (variance gamma model).

ABYSS

,The Gärtner-Ellis Theorem, Homogenization, and Affine Processes,a special family of functions having a similar Laplace principle expansion up to order one to that of the original family of measures. The construction of the special family of functions mentioned above is based on heat kernel expansions. Some of the ideas employed in the paper come from the theory