Prof. Jim Gatheral is visiting the Department of Mathematics in Bologna for the next two months. On September 29 and October 13 he will deliver two seminars in presence in Bologna in Aula Cremona, main building of the Math Department. You are all kindly invited. It will be possible to follow the seminars online via Zoom too (please find below the links to connect).

or Zoom https://unibo.zoom.us/j/99763851456?pwd=YzVBMTNxUXpRWngrNExaRWtMRjRkdz09

Title: Diamond trees and the forest expansion

Abstract: I will present a “broken exponential martingale” G-expansion that generalizes and unifies our earlier exponentiation result (Alòs, Gatheral, and Radoičić) and the cumulant recursion formula of Lacoin, Rhodes, and Vargas. As one application, I show how to compute all terms in an expansion of the Lévy area. By reordering the trees in the G-expansion according to the number of leaves, our earlier exponentiation theorem can be recovered. As further applications, I will give model-free expressions for various quantities of interest under stochastic volatility. Finally, I will exhibit explicit computations of diamond trees under rough Heston.

13-Oct-2021 16:00 (CET time) Aula Cremona, Department of Mathematics
or Zoom https://unibo.zoom.us/j/91206042957?pwd=d21ybkJQTEtkZHRWd25RLzJOQWV0QT09

Title: Pricing in affine forward variance models

Abstract: The class of affine forward variance (AFV) models was defined in Gatheral and Keller-Ressel (2019); this class includes both the conventional Heston model and its celebrated extension, the rough Heston model of El Euch and Rosenbaum. The AFV characteristic function may be expressed in terms of the solution of a Volterra integral equation. I will present a rational approximation to the solution of this integral equation in the special case of the rough Heston model. Until now, simulation of AFV models using the Markovian approximation of Abi Jaber and El Euch has proved relatively complicated and time-consuming, I will present a new efficient and easy-to-implement method for simulating AFV models for general kernels. I will present numerical results using the rational approximation as a benchmark.