Stochastic Modeling of Power Markets Using Stationary Processes

Benth, Fred Espen; Eyjolfsson, Heidar

doi:10.1007/978-3-0348-0545-2_14

Cited by 6 publications

(12 citation statements)

References 15 publications

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“…Indeed, one can always find such an approximation, since the space of continuous functions with compact support is dense in any L p space where 1 ≤ p < ∞ (see Proposition 7.9 in Folland [16]). Now, having imposed such a continuity condition, let us point out some of the advantages of employing our method for obtaining trajectories of LSS processes, as opposed to numerical integration or the Euler method discussed by Benth and Eyjolfsson in [10].…”

Section: Comparison To Other Methodsmentioning

confidence: 99%

“…This yields a convergence rate of (Δt) 2 , the same as for our Fourier method from the previous section. Furthermore, as we have mentioned, in [10] the authors present an iterative Euler-type scheme for simulating trajectories of LSS processes. The basic idea behind the scheme is to assume that there exists a positive function h :…”

Section: So By Joining the Above Manipulations Withmentioning

confidence: 99%

“…Thus a Lévy semistationary processes which is modulated by a stationary volatility process can be thought of as a stationary analogue of Lévy semimartingales of the type t → t 0 σ(s)dL(s). Benth and Eyjolfsson [10] discuss numerical methods for simulating discrete trajectories of Lévy semistationary processes, albeit without studying the corresponding approximation errors. The current paper reintroduces an approximation method presented in that paper and analyzes its convergence.…”

Section: Introductionmentioning

confidence: 99%

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Approximating Lévy Semistationary Processes via Fourier Methods in the Context of Power Markets

Benth¹,

Eyjolfsson²,

Veraart³

2014

SIAM J. Finan. Math.

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The present paper discusses simulation of Lévy semistationary (LSS) processes in the context of power markets. A disadvantage of applying numerical integration to obtain trajectories of LSS processes is that such a scheme is not iterative. We address this problem by introducing and analyzing a Fourier simulation scheme for obtaining trajectories of these processes in an iterative manner. Furthermore, we demonstrate that our proposed scheme is well suited for simulation of a wide range of LSS processes, including, in particular, LSS processes indexed by a kernel function which is steep close to the origin. Finally, we put our simulation scheme to work for simulating the price of path-dependent options to demonstrate the advantages of the proposed Fourier simulation scheme.

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Section: Comparison To Other Methodsmentioning

confidence: 99%

Section: So By Joining the Above Manipulations Withmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximating Lévy Semistationary Processes via Fourier Methods in the Context of Power Markets

Benth¹,

Eyjolfsson²,

Veraart³

2014

SIAM J. Finan. Math.

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“…Now under the assumption that the stochastic processes {a(t)} t∈R and {σ(t)} t∈R are independent to each other and the driving Lévy process {L(t)} t∈R , we have the following result for LSS processes of the type (2.1), which is based on a result in [5].…”

Section: Volatility Modulated Volterra Processesmentioning

confidence: 99%

Simulation of volatility modulated Volterra processes using hyperbolic stochastic partial differential equations

Benth¹,

Eyjolfsson²

2016

Bernoulli

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We propose a finite difference scheme to simulate solutions to a certain type of hyperbolic stochastic partial differential equation (HSPDE). These solutions can in turn estimate so called volatility modulated Volterra (VMV) processes and Lévy semistationary (LSS) processes, which is a class of processes that have been employed to model turbulence, tumor growth and electricity forward and spot prices. We will see that our finite difference scheme converges to the solution of the HSPDE as we take finer and finer partitions for our finite difference scheme in both time and space. Finally, we demonstrate our method with an example from the energy finance literature.

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“…More specifically, it is our goal is to extend the Fourier approximation methods first introduced in the setting of power markets by Benth and Eyjolfsson [9] and analysed further in Benth et al [10] in the setting of null-spatial ambit fields, called Lévy semistationary processes, to more general ambit fields. Thus we first give a general introduction to ambit fields and how they are defined, after which we introduce the Fourier approximation method in the setting of ambit fields.…”

Section: Introductionmentioning

confidence: 99%

Approximating ambit fields via Fourier methods

Eyjolfsson

2015

Stochastics

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In their paper employ so called ambit fields to model electricity spot-forward dynamics. We briefly introduce and discuss ambit fields, and introduce a novel method for approximating general ambit fields by a linear combination of ambit fields driven by exponential kernel functions (as has already been done in the null-spatial case of Lévy semistationary processes by Benth et al. [11]) by approximating the deterministic kernel function by a carefully selected finite sum. Moreover, we shall study examples, in the setting of modelling electricity forward markets, of ambit fields with singular kernel functions to illustrate the usefulness of our method for pricing purposes.

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Stochastic Modeling of Power Markets Using Stationary Processes

Cited by 6 publications

References 15 publications

Approximating Lévy Semistationary Processes via Fourier Methods in the Context of Power Markets

Approximating Lévy Semistationary Processes via Fourier Methods in the Context of Power Markets

Simulation of volatility modulated Volterra processes using hyperbolic stochastic partial differential equations

Approximating ambit fields via Fourier methods

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