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From 1/√n to 1/n: Accelerating SDE Simulation with Cubature Formulae
Monte Carlo sampling is the standard approach for estimating properties of solutions to stochastic differential equations (SDEs), but its error decays only as 1/√n, requiring huge sample sizes. Lyons and Victoir (2004) proposed replacing independently sampled Brownian driving paths with “cubature formulae”, deterministic weighted sets of paths that match Brownian “signature moments” up to some degree D. They prove that cubature formulae exist for arbitrary D, but explicit constructions are difficult and have only reached D=7, too small for practical use.
We present an algorithm that efficiently and automatically constructs cubature formulae of arbitrary degree, reproducing D=7 in seconds and reaching D=17 within hours on modest hardware. In simulations across multiple SDEs, our cubature formulae achieve an error roughly of order 1/n, orders of magnitude smaller than Monte Carlo with the same number of paths.
Based on joint work with Thomas Coxon and James Foster.
Date:
21 October 2025, 11:00
Venue:
24-29 St Giles', 24-29 St Giles' OX1 3LB
Venue Details:
Department of Statistics; Small lecture theatre
Speaker:
Peter Koepernik (University of Oxford)
Organising department:
Department of Statistics
Part of:
Junior Probability Seminar
Booking required?:
Not required
Audience:
Members of the University only
Editor:
William Garrett
