{"paper":{"title":"Varadhan's formula, conditioned diffusions, and local volatilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","q-fin.CP"],"primary_cat":"q-fin.PR","authors_text":"Peter Friz, Stefano De Marco","submitted_at":"2013-11-06T23:08:15Z","abstract_excerpt":"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 larg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1545","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}