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math.PR2025
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…
math.PR2025
Exponentially Fading Memory Signature
Eduardo Abi Jaber, Dimitri Sotnikov
We introduce the exponentially fading memory (EFM) signature, a time-invariant transformation of an infinite (possibly rough) path that serves as a mean-reverting analogue of the c…
q-fin.MF2025★ 1 cited
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…