Efficient Computation Of Sensitivities For Derivatives In Energy Markets

Abstract

In this study, we develop a stochastic framework for computing Delta sensitivities in energy markets, where both prices and traded volumes are modeled as correlated stochastic processes. Within this framework, we analyze two complementary approaches for sensitivity analysis: the density method, which is applicable when the density of the underlying process is known, and the Malliavin calculus method, which does not require any explicit knowledge of the density and relies only on the dynamics of the processes. We present illustrative examples for both methods. For the density-based approach, we consider Ornstein-Uhlenbeck and CARMA processes to model prices and energy volumes. For the Malliavin calculus approach, we study Ornstein-Uhlenbeck processes, jump diffusion driven by a compound Poisson process, time-changed Brownian motion processes subordinated by an inverse Gaussian (IG) process, as well as Ornstein-Uhlenbeck processes driven by a normal inverse Gaussian (NIG) process. We provide some numerical examples illustrating the implementation of the proposed formulas and demonstrating a close agreement between the resulting delta estimates.