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

Quadratic Gaussian models: analytic expressions for pricing and portfolio allocation

Eduardo Abi Jaber (Université Paris 1 Panthéon-Sorbonne)

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4. Quadratic Gaussian models: analytic expressions for pricing and portfolio allocation

大阪大学 数理・データ科学セミナー 金融・保険セミナーシリーズ 第124回

Quadratic Gaussian models: analytic expressions for pricing and portfolio allocation

Eduardo Abi Jaber (Université Paris 1 Panthéon-Sorbonne)

Stochastic models based on Gaussian processes, like fractional Brownian motion, are able to reproduce important stylized facts of financial markets such as rich autocorrelation structures, persistence and roughness of sample paths. This is made possible by virtue of the flexibility introduced in the choice of the covariance function of the Gaussian process. The price to pay is that, in general, such models are no longer Markovian nor semimartingales, which limits their practical use. We derive explicit analytic expressions for Fourier-Laplace transforms of quadratic functionals of Gaussian processes. Such analytic expression can be approximated by closed form matrix expressions stemming from Wishart distributions. We highlight the applicability of such result in the context of rough volatility modeling: (i) fast pricing and calibration in the (rough) fractional Stein-Stein model; (ii) explicit solutions for the Markowitz portfolio allocation problem in a multivariate rough Stein—Stein model.

Based on joint works with Enzo Miller and Huyên Pham.