Modelling Electricity Futures by Ambit Fields

Abstract

In this paper we propose a new modelling framework for electricity futures markets based on so-called ambit fields. The new model can capture many of the stylised facts observed in electricity futures and is highly analytically tractable. We discuss martingale conditions, option pricing, and change of measure within the new model class. Also, we study the corresponding model for the spot price, which is implied by the new futures model, and show that, under certain regularity conditions, the implied spot price can be represented in law as a volatility modulated Volterra process.

Selfdecomposable Fields

“…Finally, L denotes a Lévy basis (i.e., an independently scattered and infinitely divisible random measure). For aspects of the theory and applications of ambit processes and fields, see [8,10,12,14,15,23,34,39,52] and [55].…”

“…This remark induces naturally the following definition: (11) and (12) hold. If in addition, ν does not charge zero, we say that ν is the master Lévy measure of X.…”

Empirical likelihood methods for discretely observed Gaussian moving averages

“…The numerical computation for solving equations (18) 1 (B i,4 , θ) = 0, φ 4,2 (B i,4 , θ) = 0 and φ 4,3 (B i,4 , θ) = 0 when p = 3, where φ is defined by Equation (8). Table 3 reports the means and the RMSEs of 500 realizations of the estimatorθ n for seven different kernel functions, for different choices r and M and for different N. We set the true parameter value to θ = (σ = 0.3, λ = 0.5) for the MA with kernels K(s) = e −λs 1 {s>0} , e −λ|s| , e −λ 2 s 2 and 1/(1 + λs)1 {s>0} , and set the true parameter value to θ = (σ = 3, λ = 0.5, ω = 2) for the MA with kernels K(s) = cos(ωs) e −λs 1 {s>0} and sin(ωs) e −λs 1 {s>0} .…”

“…[6] Barndorff-Nielsen and Schmiegel [7] developed the idea of Gaussian MAs further by introducing a stochastic volatility component leading to Brownian semi-stationary (BSS) processes, which are a very promising class of processes for modelling turbulence. Furthermore, these processes have also been applied to model electricity forward prices by Barndorff-Nielsen et al [8] The asymptotic behaviour of power and multipower variations of BSS processes, which can be used to construct a diagnostic tool concerning the nature of empirical process, was studied by Barndorff-Nielsen et al [9] As noted by Barndorff-Nielsen et al, [9] Gaussian MAs are an important auxiliary object in the study of BSS processes. To model the instantaneous work-load of a network device responding to a random *Email: sbzhang@shmtu.edu.cn incident flux of work requests, Wolpert and Taqqu [10] constructed a class of Gaussian MAs namely fractional Ornstein-Uhlenbeck (O-U) Gaussian processes.…”

On the approximation of Lévy driven Volterra processes and their integrals

“…For β ∈ (−1/2, 0), the integral (4) is obtained as an appropriate stochastic modification of the Riemann-Liouville fractional integral in which the factor e −λ(t−s) in the kernel has a dampening effect. The processes (4) appear explicitly in the modelling of turbulence and in the modelling of environmental risk factors in energy finance (e.g. wind), see [5,36].…”