Sensitivity analysis in the infinite dimensional Heston model

TL;DR

This paper develops sensitivity analysis methods for an infinite dimensional Heston model used in commodity forward pricing, employing Malliavin calculus to interpret Greeks in an infinite-dimensional setting.

Contribution

It introduces a novel approach to compute Greeks in an infinite dimensional stochastic volatility model using Malliavin calculus and randomization techniques.

Findings

Derived representation formulas for forward prices.

Extended Greeks computation to infinite-dimensional parameters.

Applied Malliavin calculus to interpret sensitivities in the model.

Abstract

We consider the infinite dimensional Heston stochastic volatility model proposed in \arXiv:1706:03500. The price of a forward contract on a non-storable commodity is modelled by a generalized Ornstein-Uhlenbeck process in the Filipovi\'{c} space with this volatility. We prove different representation formulas for the forward price. Then we consider prices of options written on these forward contracts and we study sensitivity analysis with computation of the Greeks with respect to different parameters in the model. Since these parameters are infinite dimensional, we need to reinterpret the meaning of the Greeks. For this we use infinite dimensional Malliavin calculus and a randomization technique.