MMDS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

Implied volatility from local volatility: A path integral approach

Tai-Ho Wang (Baruch College, The City University of New York)

大阪大学 金融・保険セミナーシリーズ 第48回(CSFI-CRESTジョイントセミナー)

Implied volatility from local volatility: A path integral approach

Tai-Ho Wang (Baruch College, The City University of New York)

We derive an exact Brownian bridge representation for the transition density in a local volatility model, which then leads to an exact expression for the transition density in terms of a path integral. In the time homogeneous case, we recover the heat kernel expansion by Taylor-expanding around the most-likely-path. Repeating the same procedure in the time inhomogeneous case leads to a new and natural approximation to the transition density which differs from the conventional heat kernel expansion. We show that by suitably approximating the path integral representation, we recover the results obtained in our previous work. Applying the methodology to higher dimension models we obtain a Bessel bridge representation for the heat kernel in the hyperbolic space. In particular, the closed form expression in the case of 3 dimensional hyperbolic space is recovered.

講師: Tai-Ho Wang (Baruch College, The City University of New York)
テーマ: 大阪大学 金融・保険セミナーシリーズ 第48回(CSFI-CRESTジョイントセミナー)
日時: 2014年01月17日(金) 16:20-17:50
場所: 大阪大学(豊中キャンパス) 大学院基礎工学研究科 I棟 I204演習(セミナー)室
参加費: 無料
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