Cross-Commodity Spot Price Modeling with Stochastic Volatility and Leverage For Energy Markets

Benth, Fred Espen; Vos, Linda

doi:10.1239/aap/1370870129

Cited by 11 publications

(5 citation statements)

References 29 publications

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“…Benth [8] proposed the BNS SV model in an exponential mean-reversion dynamics to model gas prices collected from the UK market. Later, Benth and Vos [11,12] extended this to a multifactor framework to model prices in energy markets. Their extension of the BNS SV model to a multivariate context is based on the work by Barndorff-Nielsen and Stelzer [7].…”

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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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: 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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“…Volatility clusters are often found in energy prices, see, for example, Hikspoors and Jaimungal [50], Trolle and Schwartz [64], Benth [22], Benth and Vos [26], Koopman, Ooms and Carnero [55], Veraart and Veraart [65]. Therefore, it is important to have a stochastic volatility component, given by ω, in the model.…”

Section: Stochastic Volatilitymentioning

confidence: 99%

Modelling Energy Spot Prices by Volatility Modulated Lévy-Driven Volterra Processes

2012

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This paper introduces the class of volatility modulated Lévy-driven Volterra (VMLV) processes and their important subclass of Lévy semistationary (LSS) processes as a new framework for modelling energy spot prices. The main modelling idea consists of four principles: First, deseasonalised spot prices can be modelled directly in stationarity. Second, stochastic volatility is regarded as a key factor for modelling energy spot prices. Third, the model allows for the possibility of jumps and extreme spikes and, lastly, it features great flexibility in terms of modelling the autocorrelation structure and the Samuelson effect. We provide a detailed analysis of the probabilistic properties of VMLV processes and show how they can capture many stylised facts of energy markets. Further, we derive forward prices based on our new spot price models and discuss option pricing. An empirical example based on electricity spot prices from the European Energy Exchange confirms the practical relevance of our new modelling framework.

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“…The matrices C 1 and C 2 for the stochastic volatility process have considerably slower speeds of mean reversion. The parameters for the stochastic volatility part were inspired by the empirical study in [33]. Vos [33] fitted a two-factor BNS stochastic volatility model to Dutch stock price data.…”

Section: Simulation Of Matrix-valued Subordinatorsmentioning

confidence: 99%

“…The parameters for the stochastic volatility part were inspired by the empirical study in [33]. Vos [33] fitted a two-factor BNS stochastic volatility model to Dutch stock price data. We have applied these numbers here simply for illustration, and do not intend to claim that they are necessarily relevant for energy markets.…”

Section: Simulation Of Matrix-valued Subordinatorsmentioning

confidence: 99%