Cointegrated Commodity Markets and Pricing of Derivatives in a Non-Gaussian Framework

Benth, Fred Espen

doi:10.1007/978-3-319-45875-5_20

Cited by 5 publications

(5 citation statements)

References 28 publications

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“…we also have that λ(t)U (t) = U (t)λ(t). 2 These results do not hold in general when λ does not satisfy (CP), due to the non-commutativity of the matrix product. Now, apply Itô's Lemma to U (t)f (t):…”

Section: )mentioning

confidence: 98%

“…Since S 2 (t)/a 2 − S 1 (t)/a 1 = s 2 (t)/a 2 − s 1 (t)/a 1 + Y 2 (t)/a 2 − Y 1 (t)/a 1 , we say that S 1 and S 2 are cointegrated around the seasonality function s 2 (t)/a 2 − s 1 (t)/a 1 (cf. [2]).…”

Section: A Two-commodity Cointegrated Marketmentioning

confidence: 99%

“…We present it in the case of two commodities for the sake of simplicity, as generalizations are straightforward. We are inspired by the spot price model presented in [2]. After specifying the spot price dynamics under a martingale measure Q, we will derive forward prices by the conditional expectation.…”

Section: A Two-commodity Cointegrated Marketmentioning

confidence: 99%

“…Since S 2 (t)/a 2 − S 1 (t)/a 1 = s 2 (t)/a 2 − s 1 (t)/a 1 + Y 2 (t)/a 2 − Y 1 (t)/a 1 , we say that S 1 and S 2 are cointegrated around the seasonality function s 2 (t)/a 2 − s 1 (t)/a 1 (cf. [2]). Consistently with the notation in Section 3, we have that κ = R y 2 ν(dy) and κ i = R y 2 ν i (dy), i = 1, 2, and…”

Section: A Two-commodity Cointegrated Marketmentioning

confidence: 99%

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Mean-reverting additive energy forward curves in a Heath–Jarrow–Morton framework

2019

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One of the peculiarities of power and gas markets is the delivery mechanism of forward contracts. The seller of a futures contract commits to deliver, say, power, over a certain period, while the classical forward is a financial agreement settled on a maturity date. Our purpose is to design a Heath-Jarrow-Morton framework for an additive, mean-reverting, multicommodity market consisting of forward contracts of any delivery period. Even for relatively simple dynamics, we face the problem of finding a density between a risk-neutral measure Q, such that the prices of traded assets like forward contracts are true Q-martingales, and the real world probability P, under which forward prices are mean-reverting. By assuming that forward prices can be represented as affine functions of a universal source of randomness, we can completely characterize the models which prevent arbitrage opportunities. In this respect, we prove two results on the martingale property of stochastic exponentials. The first allows to validate measure changes made of two components: an Esscher-type density and a Girsanov transform with stochastic and unbounded kernel. The second uses a different approach and works for the case of continuous density. We show how this framework provides an explicit way to describe a variety of models by introducing, in particular, a generalized Lucia-Schwartz model and a cross-commodity cointegrated market.

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Section: )mentioning

confidence: 98%

Section: A Two-commodity Cointegrated Marketmentioning

confidence: 99%

Section: A Two-commodity Cointegrated Marketmentioning

confidence: 99%

Section: A Two-commodity Cointegrated Marketmentioning

confidence: 99%

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Mean-reverting additive energy forward curves in a Heath–Jarrow–Morton framework

2019

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“…The computation of the expectation functional can be performed using a Fourier transform approach. We refer to Benth [5] for more details on this for quanto options. Admittedly, we need a continuous-time version of the seasonality functions for both PV production and power price.…”

Section: A Continuous-time Ar(p) Dynamicsmentioning

confidence: 99%

Stochastic modeling of photovoltaic power generation and electricity prices

Benth¹,

Ibrahim²

2017

JEM

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In recent years, renewable energy has gained importance in producing power in many markets. The aim of this article is to model photovoltaic (PV) production for three transmission operators in Germany. PV power can only be generated during sun hours and the cloud cover will determine its overall production. Therefore, we propose a model that takes into account the sun intensity as a seasonal function. We model the deseasonalized data by an autoregressive process to capture the stochastic dynamics in the data. We present two applications based on our suggested model. First, we build a relationship between electricity spot prices and PV production where the higher the volume of PV production, the lower the power prices. As a further application, we discuss virtual power plant derivatives and energy quanto options.

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Non-Gaussian Regime-Switching Model in Application to the Commodity Price Description

Szarek

Bielak

Wyłomańska

2021

Applied Condition Monitoring

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Cointegrated Commodity Markets and Pricing of Derivatives in a Non-Gaussian Framework

Cited by 5 publications

References 28 publications

Mean-reverting additive energy forward curves in a Heath–Jarrow–Morton framework

Mean-reverting additive energy forward curves in a Heath–Jarrow–Morton framework

Stochastic modeling of photovoltaic power generation and electricity prices

Non-Gaussian Regime-Switching Model in Application to the Commodity Price Description

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