The webinars will take place on Zoom and a link to the virtual room will be sent out to all those who registered at the registration page.
Speaker: Eduardo Abi Jaber (University of Paris I: Panthéon-Sorbonne)
Title: Quadratic Gaussian models: analytic expressions for pricing and portfolio allocation
Abstract: 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.
This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to renewable energy markets and production. This series brings together the major research themes of the projects STORM, SCROLLER, and SPATUS.