大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,The University of Osaka

Asymptotics for diffusions under partial conditioning and applications to Dupire's local volatility

Stefano De Marco (Ecole Polytechnique)

1. ホーム
2. セミナー・集中講義
3. セミナー
4. Asymptotics for diffusions under partial conditioning and applications to Dupire's local volatility

大阪大学 金融・保険セミナーシリーズ 第50回(CSFI-阪大確率論セミナー共催)

Asymptotics for diffusions under partial conditioning and applications to Dupire's local volatility

Stefano De Marco (Ecole Polytechnique)

Motivated by marginals-mimicking results for Ito 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 $X =(Y,Z)$. 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 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.
Joint work with P. Friz.