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


Stefano De Marco (Ecole Polytechnique)
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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.

講 師:
Stefano De Marco (Ecole Polytechnique)
テーマ:
Asymptotics for diffusions under partial conditioning and applications to Dupire's local volatility
日 時:
2014年04月01日(火)16:30-18:00
場 所:
大阪大学(豊中キャンパス) 大学院理学研究科 E棟 E301大セミナー室
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無料
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