@article{Deuschel:2013:10.1002/cpa.21478,
author = {Deuschel, JD and Friz, PK and Jacquier, A and Violante, S},
doi = {10.1002/cpa.21478},
journal = {Communications on Pure and Applied Mathematics},
title = {Marginal density expansions for diffusions and stochastic volatility, Part I: Theoretical foundations},
url = {http://dx.doi.org/10.1002/cpa.21478},
volume = {n/a},
year = {2013}
}

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TY  - JOUR
AB  - Density expansions for hypoelliptic diffusions $(X^1,...,X^d)$ are revisited.In particular, we are interested in density expansions of the projection$(X_T^1,...,X_T^l)$, at time $T>0$, with $l \leq d$. Global conditions arefound which replace the well-known "not-in-cutlocus" condition known fromheat-kernel asymptotics; cf. G. Ben Arous (1988). Our small noise expansionallows for a "second order" exponential factor. Applications include tail andimplied volatility asymptotics in some correlated stochastic volatility models;in particular, we solve a problem left open by A. Gulisashvili and E.M. Stein(2009).
AU  - Deuschel,JD
AU  - Friz,PK
AU  - Jacquier,A
AU  - Violante,S
DO  - 10.1002/cpa.21478
PY  - 2013///
SN  - 0010-3640
TI  - Marginal density expansions for diffusions and stochastic volatility, Part I: Theoretical foundations
T2  - Communications on Pure and Applied Mathematics
UR  - http://dx.doi.org/10.1002/cpa.21478
UR  - http://arxiv.org/abs/1111.2462v1
VL  - n/a
ER  - 

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