Varadhan's formula, conditioned diffusions, and local volatilities

14 Jun 2016  ·  De Marco Stefano, Friz Peter ·

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 $\mathcal{L}(Z_t|Y_t = y)$ 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. read more

PDF Abstract
No code implementations yet. Submit your code now



  Add Datasets introduced or used in this paper

Results from the Paper

  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.


No methods listed for this paper. Add relevant methods here