Polynomial Processes for Power Prices

  title={Polynomial Processes for Power Prices},
  author={T. Ware},
  journal={Applied Mathematical Finance},
  pages={453 - 474}
  • T. Ware
  • Published 1 October 2017
  • Mathematics
  • Applied Mathematical Finance
ABSTRACT Polynomial processes have the property that expectations of polynomial functions (of degree n, say) of the future state of the process conditional on the current state are given by polynomials (of degree ≤ n) of the current state. Here we explore the potential of polynomial maps of polynomial processes for modelling energy prices. We focus on the example of Alberta power prices, derive one- and two-factor models for spot prices. We examine their performance in numerical experiments… 
Pricing of Commodity and Energy Derivatives for Polynomial Processes
This work derives a tailor-made framework for efficient polynomial approximation of the main derivatives encountered in commodity and energy markets, encompassing a wide range of arithmetic and geometric models.
Correlators of Polynomial Processes
In the setting of polynomial jump-diffusion dynamics, we provide a formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula
PR ] 2 6 Ju n 20 19 Correlators of Polynomial Processes
A process is polynomial if its extended generator maps any polynomial to a polynomial of equal or lower degree. Then its conditional moments can be calculated in closed form, up to the computation of
Abstract polynomial processes.
We suggest a novel approach to polynomial processes solely based on a polynomial action operator. With this approach, we can analyse such processes on general state spaces, going far beyond Banach
Markov Cubature Rules for Polynomial Processes
Markov cubature rules aid the tractability of path-dependent tasks such as American option pricing in models where the underlying factors are polynomial processes.
Probability measure-valued jump-diffusions in finance and related topics
The martingale problem is known to be a classical and very powerful technology for the study of Markov processes through the analytical properties of the corresponding generators. This approach
M F ] 2 1 Ju l 2 01 9 Polynomial Jump-Diffusion Models ∗
We develop a comprehensive mathematical framework for polynomial jump-diffusions in a semimartingale context, which nest affine jump-diffusions and have broad applications in finance. We show that
Polynomial Jump-Diffusion Models
A large class of novel financial asset pricing models that are based on polynomial jump-diffusions are introduced, including a generic method for option pricing based on moment expansions.
Solution of integrals with fractional Brownian motion for different Hurst indices
In this paper, we will evaluate integrals that define the conditional expectation, variance and characteristic function of stochastic processes with respect to fractional Brownian motion (fBm) for all
A Multifactor Polynomial Framework for Long-Term Electricity Forwards with Delivery Period
A rolling hedge is suggested which only uses liquid forward contracts and is risk-minimizing in the sense of F\"ollmer and Schweizer and can be calibrated to observed electricity forward curves easily and well.


Polynomial processes and their applications to mathematical finance
We introduce a class of Markov processes, called m-polynomial, for which the calculation of (mixed) moments up to order m only requires the computation of matrix exponentials. This class contains
Diffusion Processes with Polynomial Eigenfunctions
The aim of this paper is to characterize the one-dimensional stochastic differential equations, for which the eigenfunctions of the infinitesimal generator are polynomials in y. Affine
Stochastic Behaviour of the Electricity Bid Stack: From Fundamental Drivers to Power Prices
We develop a fundamental model for spot electricity prices, based on stochastic processes for underlying factors (fuel prices, power demand and generation capacity availability), as well as a
A 'simple' hybrid model for power derivatives
Polynomial diffusions and applications in finance
This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest
Electricity price modeling and asset valuation: a multi-fuel structural approach
We introduce a new and highly tractable structural model for spot and derivative prices in electricity markets. Using a stochastic model of the bid stack, we translate the demand for power and the
Short-Term Variations and Long-Term Dynamics in Commodity Prices
In this article, we develop a two-factor model of commodity prices that allows meanreversion in short-term prices and uncertainty in the equilibrium level to which prices revert. Although these two
An Interest Rate Model with Upper and Lower Bounds
We propose a new interest rate dynamicsmodel where the interest rates fluctuate in a bounded region. The model ischaracterised by five parameters which are sufficiently flexible to reflect