Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations
By Jean-Dominique Deuschel, Peter K. Friz, Antoine Jacquier, S. Violante. 2011
54 citations recorded by the source corpus.
Density expansions for hypoelliptic diffusions (X1,…,Xd) are revisited. We are particularly interested in density expansions of the projection ( XT1,⋯,XTl) at time T > 0 with l ≤ d. Global conditions are found that replace the well‐known “not‐in‐cut‐locus” condition known from heat kernel asymptotics. Our small‐noise expansion allows for a “second order” exponential factor. As an application, new light is shed on the Takanobu‐Watanabe expansion of Brownian motion and Lévy's stochastic area. Further applications include tail and implied volatility asymptotics in some stochastic volatility models, discussed in the companion paper .© 2013 Wiley Periodicals, Inc.
Subfields: Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e3af5ede5efd155de7caf7e0cb576ac2ba19997b
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In Finance
- Benjamin Stemper
- Christian Bayer
- Peter K. Friz
- Jorg Martin
- Paul Gassiat
- Nicolas Victoir
- Terry Lyons
- T. Cass
In Mathematical Physics
- Christian Bayer
- Benjamin Stemper
- Jorg Martin
- Paul Gassiat
- Peter K. Friz
- Nicolas Victoir
- Massimiliano Gubinelli
- Martin Hairer
Citations in the corpus
- A regularity structure for rough volatility (2017, methodology): “2004; Deuschel et al., 2014a; Deuschel, Friz, Jacquier, & Violante, 2014b), are then lost. A partial remedy here is to move from large deviations to (higher order) moderate deviations. Analytic tractability is so restored and one still captures the main feature of the volatility smile close to the m”