A Non-Gaussian Ornstein-Uhlenbeck Model for Pricing Wind Power Futures

Abstract

The recent introduction of wind power futures written on the German wind power production index has brought with it new interesting challenges in terms of modeling and pricing. Some particularities of this product are the strong seasonal component embedded in the underlying, the fact that the wind index is bounded from both above and below, and also that the futures are settled against a synthetically generated spot index. Here, we consider the non-Gaussian Ornstein-Uhlenbeck type processes proposed by Barndorff-Nielsen and Shephard (2001) in the context of modeling the wind power production index. We discuss the properties of the model and estimation of the model parameters. Further, the model allows for an analytical formula for pricing wind power futures. We provide an empirical study, where the model is calibrated to 37 years of German wind power production index that is synthetically generated assuming a constant level of installed capacity. Also, based on one year of observed prices for wind power futures with different delivery periods, we study the market price of risk. Generally, we find a negative risk premium whose magnitude decreases as the length of the delivery period increases. To further demonstrate the benefits of our proposed model, we address the pricing of European options written on wind power futures, which can be achieved through Fourier techniques.

Fast simulation of tempered stable Ornstein–Uhlenbeck processes

“…In addition, several approaches based on Lévy processes such as the Variance Gamma (VG) or the Normal Inverse Gaussian (NIG) have been proposed to overcome the known limits of the usual Black-Scholes model (see Madan andSeneta 1990 andBarndorff-Nielsen 1998): all these non Gaussian noises can of course be adopted as the drivers of OU processes. Example of their applications to mathematical finance can be found in Benth and Pircalabu (2018), Sabino (2020a) and Sabino and Cufaro Petroni (2021b) in the context of energy markets, in Bianchi and Fabozzi (Aug 2015) for the modeling of credit risk and in Barndorff-Nielsen and Shephard (2001) for stochastic volatility modeling.…”

Extremes of Lévy-driven spatial random fields with regularly varying Lévy measure

“…Theorem 1. Let (X v ) v∈R d be a Lévy-driven field given by (5) where the Lévy basis Λ and the kernel function f satisfy either Assumption 1 or Assumption 2. Let B ⊆ R d be a fixed bounded set.…”

“…In this theorem, and in the remainder of the paper, we use the notation y + = y1 {y≥0} and y γ + = (y + ) γ for any y ∈ R. Theorem 2. Let (X v ) v∈R d be a Lévy-driven field given by (5) where the Lévy basis Λ and the kernel function f satisfy either Assumption 1 or Assumption 2. Let B ⊆ R d be a fixed bounded set, and let…”

“…a Lévy basis) and f is an appropriate kernel function; see [17,Theorem 2.7] for necessary and sufficient conditions guaranteeing its existence. Lévy-driven models as in (1) form a very general modeling framework used for a wide range of purposes, including modeling of financial assets ( [4]), turbulent flows ( [3]), brain imaging data ( [13]) and wind power prices ( [5]). Estimators for its mean and variogram are suggested in [20], and central limit theorems for these estimators are also presented.…”

Model risk regarding monthly wind energy production for the valuation of a wind farm investment

“…By contrast, Chen et al (2010) apply the ARIMA time-series approach to an hourly wind power time series, while Verdejo et al (2016) use a log-normal distribution of the wind power, where its logarithm is modeled by means of an Ornstein-Uhlenbeck process. A similar approach is used by Benth and Pircalabu (2018) for the pricing of wind power futures. These models for wind power output consider different properties such as seasonality, autoregression and normal or log-normal distribution.…”