Risk valuation of quanto derivatives on temperature and electricity

ArXiv ID: 2310.07692 “View on arXiv”

Authors: Unknown

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 Lévy 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).

Keywords: Ornstein-Uhlenbeck Process, Normal Inverse Gaussian Lévy Process, Quanto Derivatives, Weather Derivatives, Conditional Least Squares, Commodities (Electricity) & Derivatives

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail
  • Why: The paper presents advanced stochastic calculus including non-homogeneous Ornstein-Uhlenbeck processes with Normal Inverse Gaussian Lévy drivers, explicit derivative pricing formulas, and static hedging strategies, reflecting high mathematical complexity. It demonstrates empirical rigor through parameter estimation via Conditional Least Squares on real electricity and temperature data, goodness-of-fit tests, and comparisons with Monte Carlo simulations.
  flowchart TD
    A["Research Goal<br>Model & Price Quanto<br>Temperature-Electricity Derivatives"] --> B["Model Development<br>Non-Homogeneous OU + NIG Lévy Process<br>for Coupled Prices & Temperature"]
    B --> C["Parameter Estimation<br>Conditional Least Squares on Real Data"]
    C --> D["Valuation & Computation<br>Explicit/Semi-Explicit Formulas &<br>Monte Carlo Validation"]
    D --> E["Risk Management<br>Static Hedging Strategies<br>via Energy & Weather Options"]
    E --> F["Key Outcomes<br>Accurate Pricing & Efficient<br>Risk Management for Quanto Products"]