Correlators of Polynomial Processes

Abstract

In the setting of polynomial jump-diffusion dynamics, we provide a formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula involves only linear combinations of the exponential of the so-called generator matrix, extending the well-known moment formula for polynomial processes. The developed framework allows to replace costly simulations with more accurate estimates, and it may be used for increasing the accuracy in financial pricing, such as for path-dependent options or in a stochastic volatility models context.