Marginal density expansions for diffusions and stochastic volatility, part II: Applications [to the Stein--Stein model]

2013/05/29 by Deuschel, J. D., Friz, P. K., Jacquier, A. +1
#60H30 #91G80 #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR)

paper · doi:10.48550/arxiv.1305.6765

Abstract

In the compagnion paper [Marginal density expansions for diffusions and stochastic volatility, part I] we discussed density expansions for multidimensional diffusions (X¹,...,X^d), at fixed time T and projected to their first l coordinates, in the small noise regime. Global conditions were found which replace the well-known "not-in-cutlocus" condition known from heat-kernel asymptotics. In the present paper we discuss financial applications; these include tail and implied volatility asymptotics in some correlated stochastic volatility models. In particular, we solve a problem left open by A. Gulisashvili and E.M. Stein (2009).

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