Motivated by marginals-mimicking results for It\^o processes via SDEs and by their applications to volatility modeling in finance, we discuss the weak convergence of the law of a hypoelliptic diffusions conditioned to belong to a target affine subspace at final time, namely L(Z_t|Y_t = y) if X_{\cdot}=(Y_\cdot,Z_{\cdot}). To do so, we revisit Varadhan-type estimates in a small-noise regime  , studying the density of the lower-dimensional component Y. The application to stochastic volatility models include the small-time and, for certain models, the large-strike asymptotics of the Gyongy-Dupire's local volatility function , the final product being asymptotic formulae that can (i) motivate parameterizations of the local volatility surface and (ii) be used to extrapolate local volatilities in a given model.
Motivated by marginals-mimicking results for It\^o processes via SDEs and by their applications to volatility modeling in finance, we discuss the weak convergence of the law of a hypoelliptic diffusions conditioned to belong to a target affine subspace at final time, namely L(Z_t|Y_t = y) if X_{\cdot}=(Y_\cdot,Z_{\cdot}). To do so, we revisit Varadhan-type estimates in a small-noise regime (as opposed to small-time) , studying the density of the lower-dimensional component Y. The application to stochastic volatility models include the small-time and, for certain models, the large-strike asymptotics of the Gyongy-Dupire's local volatility function . The final product are asymptotic formulae that can (i) motivate parameterizations of the local volatility surface and (ii) be used to extrapolate local volatilities in a given model.
A
(as opposed to small-time)
R
, the final product being
. The final product are