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,Osaka University

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

Stefano De Marco (Ecole Polytechnique)

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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.