Approximating ambit fields via Fourier methods

Abstract

In their paper employ so called ambit fields to model electricity spot-forward dynamics. We briefly introduce and discuss ambit fields, and introduce a novel method for approximating general ambit fields by a linear combination of ambit fields driven by exponential kernel functions (as has already been done in the null-spatial case of Lévy semistationary processes by Benth et al. [11]) by approximating the deterministic kernel function by a carefully selected finite sum. Moreover, we shall study examples, in the setting of modelling electricity forward markets, of ambit fields with singular kernel functions to illustrate the usefulness of our method for pricing purposes.

Representation and approximation of ambit fields in Hilbert space

“…The scheme is formulated in the state space of the Hambit field, and under certain Lipschitz conditions on the kernel function the convergence rate of the scheme is controlled. Our results provide a framework for numerical studies of ambit fields, taking a different route than the Fourier-based method suggested by Eyjolfsson [16].…”