A bivariate Normal Inverse Gaussian process with stochastic delay: efficient simulations and applications to energy markets

TL;DR

This paper introduces a new bivariate Normal Inverse Gaussian process with stochastic delays, offering an efficient simulation method that improves upon existing schemes, and applies it to energy market modeling and spread option pricing.

Contribution

The paper develops a novel bivariate NIG process with stochastic delays and a new simulation scheme that avoids acceptance-rejection, enhancing modeling and computational efficiency.

Findings

Improved simulation scheme for bivariate NIG processes.

Effective application to energy market modeling.

Accurate spread option pricing using Monte Carlo and Fourier methods.

Abstract

Using the concept of self-decomposable subordinators introduced in Gardini et al. [11], we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme that relies on the mathematical connection between self-decomposable Inverse Gaussian laws and L\'evy-driven Ornstein-Uhlenbeck processes with Inverse Gaussian stationary distribution. We show that our approach provides an improvement to the existing simulation scheme detailed in Zhang and Zhang [23] because it does not rely on an acceptance-rejection method. Eventually, these results are applied to the modelling of energy markets and to the pricing of spread options using the proposed Monte Carlo scheme and Fourier techniques