4 papers
Malliavin calculus for signatures with applications to finance
Eduardo Abi Jaber, Clément Rey, Dimitri Sotnikov
Malliavin calculus is a powerful and general framework for the analysis of square-integrable random variables, but it often suffers from a lack of tractability and explicit represe…
Efficient Simulation of Hawkes Processes using their Affine Volterra Structure
Eduardo Abi Jaber, Elie Attal, Dimitri Sotnikov
We introduce a novel and efficient simulation scheme for Hawkes processes on a fixed time grid, leveraging their affine Volterra structure. The key idea is to first simulate the in…
Martingale property and moment explosions in signature volatility models
Eduardo Abi Jaber, Paul Gassiat, Dimitri Sotnikov
We study the martingale property and moment explosions of a signature volatility model, where the volatility process of the log-price is given by a linear form of the signature of…
Heath-Jarrow-Morton meet lifted Heston in energy markets for joint historical and implied calibration
Eduardo Abi Jaber, Soukaïna Bruneau, Nathan De Carvalho +2
In energy markets, joint historical and implied calibration is of paramount importance for practitioners, yet notoriously challenging due to the need to align historical correlatio…