Correlators of Polynomial Processes

Fred Espen Benth, Silvia Lavagnini

Published 2019-06-26Version 1

A process is polynomial if its extended generator maps any polynomial to a polynomial of equal or lower degree. Then its conditional moments can be calculated in closed form, up to the computation of the exponential of the so-called generator matrix. In this article, we provide an explicit formula to the problem of computing correlators, that is, computing the expected value of moments of the process at different time points along its path. The strength of our formula is that it only involves linear combinations of the exponential of the generator matrix, as in the one-dimensional case. The framework developed allows then for easy-to-implement solutions when it comes to financial pricing, such as for path-dependent options or in a stochastic volatility models context.