Pricing and hedging of energy spread options and volatility modulated Volterra processes

TL;DR

This paper develops a model for pricing and hedging energy spread options where the underlying assets follow complex volatility modulated Volterra processes, relevant for power and gas markets, using Fourier transforms and forward prices.

Contribution

It introduces a novel pricing framework for spread options with assets modeled by volatility modulated Volterra processes, including a quadratic hedging approach.

Findings

Derived a pricing formula using Fourier transforms and characteristic functions.

Expressed spread option prices in terms of forward prices.

Provided a linear system for quadratic hedging of the options.

Abstract

We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of power and gas. Volatility modulated Volterra processes are in general not semimartingales, but contain several special cases of interest in energy markets like for example continuous-time autoregressive moving average processes. Based on a change of measure, we obtain a pricing expression based on a univariate Fourier transform of the payoff function and the characteristic function of the price dynamics. Moreover, the spread option price can be expressed in terms of the forward prices on the underlying dynamics assets. We compute a linear system of equations for the quadratic hedge for the spread option in terms of a portfolio of underlying forward contracts.