Jump-diffusion modeling in emission markets

TL;DR

This paper explores jump-diffusion models for emission allowance prices in emission markets, incorporating shocks and providing numerical methods to evaluate derivatives in these financial markets.

Contribution

It introduces jump-diffusion models for emission prices and develops numerical techniques to solve the resulting complex equations, enhancing pricing accuracy.

Findings

Jump-diffusion models capture shocks in emission prices.

Finite difference methods effectively solve the models.

Numerical results demonstrate model applicability.

Abstract

Mandatory emission trading schemes are being established around the world. Participants of such market schemes are always exposed to risks. This leads to the creation of an accompanying market for emission-linked derivatives. To evaluate the fair prices of such financial products, one needs appropriate models for the evolution of the underlying assets, emission allowance certificates. In this paper, we discuss continuous time diffusion and jump-diffusion models, the latter enabling one to model information shocks that cause jumps in allowance prices. We show that the resulting martingale dynamics can be described in terms of non-linear partial differential and integro-differential equations and use a finite difference method to investigate numerical properties of their discretizations. The results are illustrated by a small numerical study.