Risk valuation of quanto derivatives on temperature and electricity

TL;DR

This paper introduces a coupled stochastic model for electricity prices and temperature to evaluate and hedge quanto derivatives, providing explicit formulas and estimation methods validated on real data.

Contribution

It develops a novel coupled Ornstein-Uhlenbeck model with dependence for pricing and hedging quanto weather and energy derivatives.

Findings

Explicit formulas for derivative pricing are derived.

The model effectively captures dependence between temperature and electricity prices.

Hedging strategies are proposed using portfolios of electricity and temperature options.

Abstract

This paper develops a coupled model for day-ahead electricity prices and average daily temperature which allows to model quanto weather and energy derivatives. These products have gained on popularity as they enable to hedge against both volumetric and price risks. Electricity day-ahead prices and average daily temperatures are modelled through non homogeneous Ornstein-Uhlenbeck processes driven by a Brownian motion and a Normal Inverse Gaussian L\'evy process, which allows to include dependence between them. A Conditional Least Square method is developed to estimate the different parameters of the model and used on real data. Then, explicit and semi-explicit formulas are obtained for derivatives including quanto options and compared with Monte Carlo simulations. Last, we develop explicit formulas to hedge statically single and double sided quanto options by a portfolio of electricity options and temperature options (CDD or HDD).