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Fred Espen Benth

Publications and source records attributed to Fred Espen Benth.

At least 19 recordsLinked to original sources
arXiv2026

Efficient Computation Of Sensitivities For Derivatives In Energy Markets

In this study, we develop a stochastic framework for computing Delta sensitivities in energy markets, where both prices and traded volumes are modeled as correlated stochastic processes. Within this framework, we analyze two complementary approaches for sensitivity analysis: the density method, which is applicable when the density of the underlying process is known, and the Malliavin calculus method, which does not require any explicit knowledge of the density and relies only on the dynamics of the processes. We present illustrative examples for both methods. For the density-based approach, we consider Ornstein-Uhlenbeck and CARMA processes to model prices and energy volumes. For the Malliavin calculus approach, we study Ornstein-Uhlenbeck processes, jump diffusion driven by a compound Poisson process, time-changed Brownian motion processes subordinated by an inverse Gaussian (IG) process, as well as Ornstein-Uhlenbeck processes driven by a normal inverse Gaussian (NIG) process. We provide some numerical examples illustrating the implementation of the proposed formulas and demonstrating a close agreement between the resulting delta estimates.

math.PR↗
arXiv2026

Signature McKean-Vlasov stochastic differential equations

McKean-Vlasov-type stochastic differential equations (SDEs) are characterized by coefficients depending on both the state and the law of the solution. In this work, we focus on a class of such equations where the coefficients depend on a linear combination of the expected signature of the geometric $p$-rough path lift of its solution, with $p\in(2,3)$. After establishing the strong existence and uniqueness of a solution, we prove how such an equation can approximate a general class of path-dependent McKean-Vlasov SDEs. Finally, we consider the associated particle system and propagation of chaos is established.

math.PR↗
arXiv2026

Forecasting of volatility and risk premia in electricity markets

We study forecasting of the realized covariation in electricity markets. The realized covariation in this context is a matrix-valued representation of the latent infinite-dimensional covariance operator and a parsimonious matrix-HAR type model is constructed to facilitate estimation. We test the model on one-week ahead forecasts of the weekly realized covariation and find that the inclusion of longer time horizons and renewable generation information adds important predictive power. We also investigate the prediction of risk premia in electricity forward markets and find that our variance forecasts provide substantially improved forecasts of spread risk premia compared to standard methods relying on backward looking volatility.

q-fin.GN↗
arXiv2026

The fine structure of electricity price volatility

We conduct the first rigorous study of electricity price volatility for the full panel of electricity prices across three European generation zones. By interpreting the observed day-ahead prices as local averages of a latent price process governed by a stochastic partial differential equation, we develop estimators of the weekly integrated variance. The inherently infinite dimensional setting introduce several complications that are not relevant in the conventional finite dimensional semimartingale setting, and we spend considerable effort in dealing with these. In particular, we must account for both mean-reversion in prices and semigroup-smoothing in the estimated variance. We provide a detailed decomposition and interpretation of the empirical estimates across three vastly different European generation zones, namely Germany, Norway, and Spain. Our findings indicate that each zone has very different drivers of volatility, and that the impact of generation variables differs considerably. We document that leverage effects appear to be present at first sight, but disappear once we condition on suitable state variables, thereby showing that electricity price volatility does not generally exhibit asymmetric responses to price shocks.

q-fin.GN↗
arXiv2026

Numerical valuation of European options under two-asset infinite-activity exponential Lévy models

We propose a numerical method for the valuation of European-style options under two-asset infinite-activity exponential Lévy models. Our method extends the effective approach developed by Wang, Wan & Forsyth (2007) for the 1-dimensional case to the 2-dimensional setting and is applicable for general Lévy measures under mild assumptions. A tailored discretization of the non-local integral term is developed, which can be efficiently evaluated by means of the fast Fourier transform. For the temporal discretization, the semi-Lagrangian theta-method is employed in a convenient splitting fashion, where the diffusion term is treated implicitly and the integral term is handled explicitly by a fixed-point iteration. Numerical experiments for put-on-the-average options under Normal Tempered Stable dynamics reveal favourable second-order convergence of our method whenever the exponential Lévy process has finite-variation.

math.NA↗
arXiv2026

Numerical methods for solving PIDEs arising in swing option pricing under a two-factor mean-reverting model with jumps

This paper concerns the numerical valuation of swing options with discrete action times under a linear two-factor mean-reverting model with jumps. The resulting sequence of two-dimensional partial integro-differential equations (PIDEs) are convection-dominated and possess a nonlocal integral term due to the presence of jumps. Further, the initial function is nonsmooth. We propose various second-order numerical methods that can adequately handle these challenging features. The stability and convergence of these numerical methods are analysed theoretically. By ample numerical experiments, we confirm their second-order convergence behaviour.

math.NA↗
arXiv2025

Universal approximation on non-geometric rough paths and applications to financial derivatives pricing

We present a novel perspective on the universal approximation theorem for rough path functionals, introducing a polynomial-based approximation class. We extend universal approximation to non-geometric rough paths within the tensor algebra. This development addresses critical needs in finance, where no-arbitrage conditions necessitate Itô integration. Furthermore, our findings motivate a hypothesis for payoff functionals in financial markets, allowing straightforward analysis of signature payoffs proposed in \cite{arribas2018derivativespricingusingsignature}.

math.FA↗
arXiv2025

A Deep Learning Approach to Renewable Capacity Installation under Jump Uncertainty

We study a stochastic model for the installation of renewable energy capacity under demand uncertainty and jump driven dynamics. The system is governed by a multidimensional Ornstein-Uhlenbeck (OU) process driven by a subordinator, capturing abrupt variations in renewable generation and electricity load. Installation decisions are modeled through control actions that increase capacity in response to environmental and economic conditions. We consider two distinct solution approaches. First, we implement a structured threshold based control rule, where capacity is increased proportionally when the stochastic capacity factor falls below a fixed level. This formulation leads to a nonlinear partial integro-differential equation (PIDE), which we solve by reformulating it as a backward stochastic differential equation with jumps. We extend the DBDP solver in \cite{hure2020deep} to the pure jump setting, employing a dual neural network architecture to approximate both the value function and the jump sensitivity. Second, we propose a fully data driven deep control algorithm that directly learns the optimal feedback policy by minimizing the expected cost functional using neural networks. This approach avoids assumptions on the form of the control rule and enables adaptive interventions based on the evolving system state. Numerical experiments highlight the strengths of both methods. While the threshold based BSDE approach offers interpretability and tractability, the deep control strategy achieves improved performance through flexibility in capacity allocation. Together, these tools provide a robust framework for decision support in long term renewable energy expansion under uncertainty.

eess.SY↗
arXiv2025

Measure-Valued CARMA Processes

In this paper, we examine continuous-time autoregressive moving-average (CARMA) processes on Banach spaces driven by Lévy subordinators. We show their existence and cone-invariance, investigate their first and second order moment structure, and derive explicit conditions for their stationarity. Specifically, we define a measure-valued CARMA process as the analytically weak solution of a linear state-space model in the Banach space of finite signed measures. By selecting suitable input, transition, and output operators in the linear state-space model, we show that the resulting solution possesses CARMA dynamics and remains in the cone of positive measures defined on some spatial domain. We also illustrate how positive measure-valued CARMA processes can be used to model the dynamics of functionals of spatio-temporal random fields and connect our framework to existing CARMA-type models from the literature, highlighting its flexibility and broader applicability.

math.PR↗
arXiv2025

Trading off regional and overall energy system design flexibility in the net-zero transition

The transition to net-zero emissions in Europe is determined by a patchwork of country-level and EU-wide policy, creating coordination challenges in an interconnected system. We use an optimisation model to map out near-optimal energy system designs for 2050, focussing on the planning flexibility of individual regions while maintaining overall system robustness against different weather years, cost assumptions, and land use limitations. Our results reveal extensive flexibility at a regional level, where only few technologies (solar around the Adriatic and wind on the British Isles and in Germany) cannot be substituted. National policymakers can influence renewable energy export and hydrogen strategies significantly, provided they coordinate this with the remaining European system. However, stronger commitment to solar in Southern Europe and Germany unlocks more design options for Europe overall. These results on regional trade-offs facilitate more meaningful policy discussions which are crucial in the transition to a sustainable energy system.

eess.SY↗
arXiv2025

Driving towards net-zero: The impact of electric vehicle flexibility participation on a future Norwegian electricity system

Electric vehicle batteries have a proven flexibility potential which could serve as an alternative to conventional electricity storage solutions. EV batteries could support the balancing of supply and demand and the integration of variable renewable energy into the electricity system. The flexibility potential from electric vehicles, in distinction to conventional battery storage, depends on the vehicle user's willingness and opportunity to make their vehicle available for flexibility. This rate of participation is often not considered in studies, despite the impact electric vehicle flexibility could have on the electricity system. This work presents a modelling study of the Norwegian electricity system, demonstrating how a future net-zero electricity system can benefit from electric vehicles in terms of integrating renewables and balancing supply and demand, while considering the rate of participation. Our findings show electric vehicles' potential to eliminate the need for stationary battery storage with just 50% participation in vehicle-to-grid. We find that the flexibility of electric vehicles contributes to relative reductions in the total cost of the electricity system by almost 4% and 15% assuming 100% participation in flexible charging and vehicle-to-grid, respectively.

physics.soc-ph↗
arXiv2024

Structure-informed operator learning for parabolic Partial Differential Equations

In this paper, we present a framework for learning the solution map of a backward parabolic Cauchy problem. The solution depends continuously but nonlinearly on the final data, source, and force terms, all residing in Banach spaces of functions. We utilize Fréchet space neural networks (Benth et al. (2023)) to address this operator learning problem. Our approach provides an alternative to Deep Operator Networks (DeepONets), using basis functions to span the relevant function spaces rather than relying on finite-dimensional approximations through censoring. With this method, structural information encoded in the basis coefficients is leveraged in the learning process. This results in a neural network designed to learn the mapping between infinite-dimensional function spaces. Our numerical proof-of-concept demonstrates the effectiveness of our method, highlighting some advantages over DeepONets.

math.AP↗
arXiv2024

Installation of renewable capacities to meet emission targets and demand under uncertainty

This paper focuses on minimizing the costs related to renewable energy installations under emission constraints. We tackle the problem in three different cases. Assuming intervening once, we determine the optimal time to install and the optimal capacity expansions under uncertainty. By assuming the possibility of two or multiple interventions, we find that the optimal strategy is to intervene only once. We also prove that there are instances where capacity expansions should be delayed.

math.OC↗
arXiv2023

Spatio-temporal smoothing and dynamics of different electricity flexibility options for highly renewable energy systems -- Case study for Norway

In this article, we investigate mismatch of renewable electricity production to demand and how this is affected by flexibility options on the supply side. We assess the impact of spatial and temporal smoothing on reliability of production and whether they can reduce risks of variation. As a case study we pick a simplified (partial) representation of the Norwegian electricity system and focus on wind power. We represent regional electricity production and demand through two stochastic processes: the wind capacity factors are modelled as a two-dimensional Ornstein-Uhlenbeck process and electricity demand consists of realistic base load and temperature-induced load coming from a deseasonalised autoregressive process. We validate these processes, that we have trained on historical data, through Monte Carlo simulations allowing us to generate many statistically representative weather years. For the investigated realisations (weather years) we study deviations of production from demand under different wind capacities, and introduce different scenarios where flexibility options like storage and transmission is available. Our analysis shows that simulated loss values are reduced significantly by cooperation and any mode of flexibility. Combining storage and transmission leads to even more synergies and helps to stabilise production levels and thus adequacy of renewable power systems.

math.OC↗
arXiv2023

The heat modulated infinite dimensional Heston model and its numerical approximation

The HEat modulated Infinite DImensional Heston (HEIDIH) model and its numerical approximation are introduced and analyzed. This model falls into the general framework of infinite dimensional Heston stochastic volatility models of (F.E. Benth, I.C. Simonsen '18), introduced for the pricing of forward contracts. The HEIDIH model consists of a one-dimensional stochastic advection equation coupled with a stochastic volatility process, defined as a Cholesky-type decomposition of the tensor product of a Hilbert-space valued Ornstein-Uhlenbeck process, the mild solution to the stochastic heat equation on the real half-line. The advection and heat equations are driven by independent space-time Gaussian processes which are white in time and colored in space, with the latter covariance structure expressed by two different kernels. First, a class of weight-stationary kernels are given, under which regularity results for the HEIDIH model in fractional Sobolev spaces are formulated. In particular, the class includes weighted Matérn kernels. Second, numerical approximation of the model is considered. An error decomposition formula, pointwise in space and time, for a finite-difference scheme is proven. For a special case, essentially sharp convergence rates are obtained when this is combined with a fully discrete finite element approximation of the stochastic heat equation. The analysis takes into account a localization error, a pointwise-in-space finite element discretization error and an error stemming from the noise being sampled pointwise in space. The rates obtained in the analysis are higher than what would be obtained using a standard Sobolev embedding technique. Numerical simulations illustrate the results.

math.PR↗
arXiv2023

Multivariate continuous-time autoregressive moving-average processes on cones

In this article we study multivariate continuous-time autoregressive moving-average (MCARMA) processes with values in convex cones. More specifically, we introduce matrix-valued MCARMA processes with Lévy noise and present necessary and sufficient conditions for processes from this class to be cone valued. We derive specific hands-on conditions in the following two cases: First, for classical MCARMA on $\mathbb{R}_{d}$ with values in the positive orthant $\mathbb{R}_{d}^{+}$. Second, for MCARMA processes on real square matrices taking values in the cone of symmetric and positive semi-definite matrices. Both cases are relevant for applications and we give several examples of positivity ensuring parameter specifications. In addition to the above, we discuss the capability of positive semi-definite MCARMA processes to model the spot covariance process in multivariate stochastic volatility models. We justify the relevance of MCARMA based stochastic volatility models by an exemplary analysis of the second order structure of positive semi-definite well-balanced Ornstein-Uhlenbeck based models.

math.PR↗
arXiv2023

A feasible central limit theorem for realised covariation of SPDEs in the context of functional data

This article establishes an asymptotic theory for volatility estimation in an infinite-dimensional setting. We consider mild solutions of semilinear stochastic partial differential equations and derive a stable central limit theorem for the semigroup adjusted realised covariation (SARCV), which is a consistent estimator of the integrated volatility and a generalisation of the realised quadratic covariation to Hilbert spaces. Moreover, we introduce semigroup adjusted multipower variations (SAMPV) and establish their weak law of large numbers; using SAMPV, we construct a consistent estimator of the asymptotic covariance of the mixed-Gaussian limiting process appearing in the central limit theorem for the SARCV, resulting in a feasible asymptotic theory. Finally, we outline how our results can be applied even if observations are only available on a discrete space-time grid.

math.ST↗