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.
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.
R
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
In the setting of polynomial jump-diffusion dynamics
R
an explicit formula to the problem of
a formula for
R
that is, computing the expected value of moments of
namely, cross-moments of
R
strength of our formula is that it only involves
formula involves only
A
so-called
R
as in the one-dimensional case. The framework developed allows then for easy-to-implement solutions when it comes to
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