Derivatives Pricing in Energy Markets: An Infinite-Dimensional Approach

Benth, Fred Espen; Krühner, Paul

doi:10.1137/15100268x

Cited by 25 publications

(12 citation statements)

References 32 publications

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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 main motivation for studying Hilbert space-valued OU processes comes from the modelling of futures prices in commodity markets, where the dynamics follow a class of hyperbolic stochastic partial differential equations (see Benth and Krühner [9,10]). …”

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

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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“…Let us return to a general separable Hilbert space H. Forward and futures prices can be realized as infinite dimensional stochastic processes, which call for operator-valued stochastic volatility models (see Benth, Rüdiger and Süss [7] and Benth and Krühner [6]).…”

Section: Rough Stochastic Volatility Modelsmentioning

confidence: 99%

Infinite dimensional pathwise Volterra processes driven by Gaussian noise – Probabilistic properties and applications –

Benth

Harang

2021

Electron. J. Probab.

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We investigate the probabilistic and analytic properties of Volterra processes constructed as pathwise integrals of deterministic kernels with respect to the Hölder continuous trajectories of Hilbert-valued Gaussian processes. To this end, we extend the Volterra sewing lemma from [18] to the two dimensional case, in order to construct two dimensional operator-valued Volterra integrals of Young type. We prove that the covariance operator associated to infinite dimensional Volterra processes can be represented by such a two dimensional integral, which extends the current notion of representation for such covariance operators. We then discuss a series of applications of these results, including the construction of a rough path associated to a Volterra process driven by Gaussian noise with possibly irregular covariance structures, as well as a description of the irregular covariance structure arising from Gaussian processes time-shifted along irregular trajectories. Furthermore, we consider an infinite dimensional fractional Ornstein-Uhlenbeck process driven by Gaussian noise, which can be seen as an extension of the volatility model proposed by Rosenbaum et al. in [13].

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“…However, as noted by Mehrdoust and Noorani (2021), these options were traded on the Nord Pool energy exchange in the 1990s and they abandoned in 2000. Nevertheless, European-style options are very common in the Nord Pool market and are still traded on future contracts (see Benth and Kruhner 2015). Spark-spread option is another important class of derivatives in the electricity and gas market.…”

Section: Introductionmentioning

confidence: 99%

Electricity spot price modeling by multi-factor uncertain process: a case study from the Nordic region

2021

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In recent years, the liberalization of energy markets (especially electricity) by many countries has led to much attention being paid to their modeling. The energy market modeling under the framework of probability theory is valuable when the distribution function is close enough to the actual frequency. However, due to the complexity and variability of the world, economic reasons and changing government policies, this assumption is not applicable in some cases. Under such circumstances, we propose an uncertain two-factor model based on uncertain differential equations to evaluate the electricity spot price dynamics. Then, several essential indicators of electricity are investigated and generalized moment estimation for unknown parameters is also provided. Two case studies by using electricity data from the Oslo and Stockholm regions illustrate our approach. We also compare the proposed model with one-factor uncertain model driven by Liu process and the electricity stochastic model. A detailed numerical study illustrates the efficiency of the proposed model to evaluate electricity spot prices.

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Derivatives Pricing in Energy Markets: An Infinite-Dimensional Approach

Cited by 25 publications

References 32 publications

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

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

Infinite dimensional pathwise Volterra processes driven by Gaussian noise – Probabilistic properties and applications –

Electricity spot price modeling by multi-factor uncertain process: a case study from the Nordic region

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