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

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,A Remark on Gatheral’s ‘Most-Likely Path Approximation’ of Implied Volatility,We give a new proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we clarify the question of existence of ‘forward implied variance’ in the original derivation of Gatheral, who introduced this representation in his book ‘The Volatility Surface’.

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On Small Time Asymptotics for Rough Differential Equations Driven by Fractional Brownian Motions,We survey existing results concerning the study in small times of the density of the solution of a rough differential equation driven by fractional Brownian motions. We also slightly improve existing results and discuss some possible applications to mathematical finance.

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On Singularities in the Heston Model,In this note we provide characterization of the singularities of the Heston characteristic function. In particular, we show that all the singularities are pure imaginary.

障碍

Small-Time Asymptotics for the At-the-Money Implied Volatility in a Multi-dimensional Local Volatil, [.]) derived highly accurate analytic formulas for prices and implied volatilities of such options when the options are not at the money. We now extend these results to the ATM case. Moreover, we also derive similar formulas for the local volatility of the basket.

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,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).

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