Du
Shedule -
Séminaire des doctorants de FIME
Jules DELEMOTTE - Bergomi models with volatility memory
IHP - Bâtiment Borel
Salle Olga Ladyjenskaïa
A family of stochastic volatility models with memory in the volatility process is presented as an extension of Bergomi models. The volatility feedback accounts for two important features of equity markets that the classical time-homogeneous Bergomi models fail to capture: (a) the time-asymmetry of large positive VIX spikes, and (b) the positive VIX skews.
Inspired by the path-dependent volatility models of Chicheportiche and Bouchaud (2014) and Guyon and Lekeufack (2023) while aiming to keep the forward variance process as explicit as possible, we consider models where the instantaneous variance is a function of Ornstein-Uhlenbeck (OU) factors --which, like in Bergomi models, capture the market trend-- plus a weighted average of past instantaneous variances, which captures the volatility feedback. Convex combinations of exponential feedback weights yield handy Markov models. An expansion in small volatility of volatility, along the lines of the Bergomi-Guyon expansion, provides an approximation of the smile of model implied volatilities. Extensive numerical experiments are conducted that illustrate the properties of the models, compared to classical Bergomi models and the quintic OU model, and assess the accuracy of the smile expansion for market-calibrated parameters.