2 01 5 Varadhan ’ s formula , conditioned diffusions , and local volatilities
نویسندگان
چکیده
Motivated by marginals-mimicking results for Itô processes [15, 21] 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(Zt|Yt = y) if X· = (Y·, Z·). 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 Gyöngy–Dupire 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.
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