Modelling Electricity Forward Markets by Ambit Fields

Barndorff–Nielsen, Ole E.; Benth, Fred Espen; Veraart, Almut E. D.

doi:10.2139/ssrn.1938704

Cited by 25 publications

(35 citation statements)

References 60 publications

(64 reference statements)

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“…Then, X(t, x) can be interpreted as the futures price at time t ≥ 0 for a contract delivering the commodity at time x ≥ 0, with a dynamics specified under the Heath-JarrowMorton-Musiela (HJMM) modelling paradigm (see Heath, Jarrow and Morton [19] and Musiela [21]). We connect our general SV modelling approach to the analysis in Benth and Krühner [9,10] and the ambit field approach in Barndorff-Nielsen, Benth and Veraart [3,4]. We remark that this discussion can be extended to forward rate modelling under the HJM paradigm in fixed-income theory (see Filipovic [15] and Carmona and Theranchi [13] for an analysis of HJM models in infinite dimensions for fixed-income markets.…”

Section: Dx(t) = Ax(t) Dt + σ(T) Db(t)mentioning

confidence: 96%

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Ornstein–Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility

Benth

Rüdiger

Süß

2018

Stochastic Processes and their Applications

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ABSTRACT. We propose a non-Gaussian operator-valued extension of the Barndorff-Nielsen and Shephard stochastic volatility dynamics, defined as the square-root of an operator-valued Ornstein-Uhlenbeck process with Lévy noise and bounded drift. We derive conditions for the positive definiteness of the Ornstein-Uhlenbeck process, where in particular we must restrict to operator-valued Lévy processes with "non-decreasing paths". It turns out that the volatility model allows for an explicit calculation of its characteristic function, showing an affine structure. We introduce another Hilbert space-valued Ornstein-Uhlenbeck process with Wiener noise perturbed by this class of stochastic volatility dynamics. Under a strong commutativity condition between the covariance operator of the Wiener process and the stochastic volatility, we can derive an analytical expression for the characteristic functional of the Ornstein-Uhlenbeck process perturbed by stochastic volatility if the noises are independent. The case of operator-valued compound Poisson processes as driving noise in the volatility is discussed as a particular example of interest. We apply our results to futures prices in commodity markets, where we discuss our proposed stochastic volatility model in light of ambit fields.

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Section: Dx(t) = Ax(t) Dt + σ(T) Db(t)mentioning

confidence: 96%

“…Our stochastic volatility model serves as a motivation for an extension of the ambit field models. We refer to Barndorff-Nielsen, Benth and Veraart [3] and [4] for an application of ambit fields to energy forward price modelling.…”

Section: Application To Forward Price Modellingmentioning

confidence: 99%

Ornstein–Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility

Benth

Rüdiger

Süß

2018

Stochastic Processes and their Applications

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“…We recommend the book [13] for an exposition of various related approaches and extensions of this framework, including capturing cross-commodity correlation. More recently, Barndorff-Nielsen et al [9,8] propose a new approach for both spot and forward prices using ambit fields, and in particular Levy semi-stationary processes.…”

Section: 2mentioning

confidence: 99%

“…Assuming the stack model in (15) and (16), along with distributions given by (7) and p i by (17), the forward power price for time T delivery can be found (again using (8)) to be…”

Section: Version Bmentioning

confidence: 99%

A Survey of Commodity Markets and Structural Models for Electricity Prices

Carmona

Coulon

2013

Quantitative Energy Finance

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Abstract. The goal of this survey is to review the major idiosyncrasies of the commodity markets and the methods which have been proposed to handle them in spot and forward price models. We devote special attention to the most idiosyncratic of all: electricity markets. Following a discussion of traded instruments, market features, historical perspectives, recent developments and various modeling approaches, we focus on the important role of other energy prices and fundamental factors in setting the power price. In doing so, we present a detailed analysis of the structural approach for electricity, arguing for its merits over traditional reduced-form models. Building on several recent articles, we advocate a broad and flexible structural framework for spot prices, incorporating demand, capacity and fuel prices in several ways, while calculating closed-form forward prices throughout.

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“…Barndorff-Nielsen, Benth and Veraart [6] propose to use ambit fields, a class of spatio-temporal random fields, as an alternative modelling approach to the dynamic specification of forward curves used in the present paper. In a recent paper, Barndorff-Nielsen, Benth and Veraart [7] has extended the ambit field idea to cross-commodity market modelling and the pricing of spread options.…”

Section: Introductionmentioning

confidence: 99%

Derivatives Pricing in Energy Markets: An Infinite-Dimensional Approach

Benth

Krühner

2015

SIAM J. Finan. Math.

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ABSTRACT. Based on forward curves modelled as Hilbert-space valued processes, we analyse the pricing of various options relevant in energy markets. In particular, we connect empirical evidence about energy forward prices known from the literature to propose stochastic models. Forward prices can be represented as linear functions on a Hilbert space, and options can thus be viewed as derivatives on the whole curve. The value of these options are computed under various specifications, in addition to their deltas. In a second part, crosscommodity models are investigated, leading to a study of square integrable random variables with values in a "two-dimensional" Hilbert space. We analyse the covariance operator and representations of such variables, as well as presenting applications to pricing of spread and energy quanto options.

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Modelling Electricity Forward Markets by Ambit Fields

Cited by 25 publications

References 60 publications

Ornstein–Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility

Ornstein–Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility

A Survey of Commodity Markets and Structural Models for Electricity Prices

Derivatives Pricing in Energy Markets: An Infinite-Dimensional Approach

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