Optimal Stochastic Control and Carbon Price Formation

Carmona, René; Fehr, Max; Hinz, Juri

doi:10.1137/080736910

Cited by 88 publications

(106 citation statements)

References 7 publications

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“…However, if the future probability of a shortfall in permits becomes sufficiently low the price converges to zero as observed at the end of Phase I. In line with these considerations Carmona et al (2009) show in a numerical simulation that allowance prices are only a poor indicator of marginal abatement costs. These theoretical aspects have, to our knowledge, only been empirically investigated by Hintermann (2012) so far.…”

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confidence: 61%

Explaining European Emission Allowance Price Dynamics: Evidence from Phase II

Rickels

Görlich

Peterson

2015

German Economic Review

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In this paper we empirically investigate potential determinants of allowance (EUA) price dynamics in the European Union Emission Trading Scheme (EU ETS) during Phase II. In contrast to previous papers, we analyze a significantly longer time series, place particular emphasis on the importance of price variable selection, and include an extensive data of renewable energy feed-in in Europe. We show (i) that results are extremely sensitive to choosing different price series of potential determinants, such as coal and gas prices, (ii) that EUA price dynamics are only marginally influenced by renewable energy provision in Europe, and iii) that EUA prices currently do not reflect marginal abatement costs across Europe. We conclude that the expectation of a more mature allowance market in Phase II cannot be confirmed. In this paper we empirically investigate potential determinants of allowance (EUA) price dynamics in the European Union Emission Trading Scheme (EU ETS) during Phase II. In contrast to previous papers, we analyze a significantly longer time series, place particular emphasis on the importance of price variable selection, and include an extensive data of renewable energy feed-in in Europe. We show (i) that results are extremely sensitive to choosing different price series of potential determinants, such as coal and gas prices, (ii) that EUA price dynamics are only marginally influenced by renewable energy provision in Europe, and iii) that EUA prices currently do not reflect marginal abatement costs across Europe. We conclude that the expectation of a more mature allowance market in Phase II cannot be confirmed.

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supporting

confidence: 61%

Explaining European Emission Allowance Price Dynamics: Evidence from Phase II

Rickels

Görlich

Peterson

2015

German Economic Review

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“…As announced, we go back to the smooth setting by mollification: Example 2.9. Consider a non-decreasing function φ as in (2) and φ − and φ + as in (3). Notice that φ + is a cumulative distribution function as a non-decreasing right-continuous function matching 0 at −∞ and 1 at +∞.…”

Section: Proposition 28 Consider the Mollified Equation (5) With A mentioning

confidence: 99%

“…Assume that (A. [1][2][3][4] are in force and that φ = 1 [Λ,+∞) as in Section 3. Then, at any time t < T and for any p ∈ R d , the mapping R ∋ e ֒→ E 0,p,e t is an homeomorphism with probability 1, and with non-zero probability, it is not a homeomorphism at time t = T .…”

Section: Absolute Continuity Before Terminal Time Tmentioning

confidence: 99%

“…See for example [3,18,2,4] for mathematical models of these markets. As exemplified in [1], the components of the stochastic process P can be viewed as the prices of the goods whose production is the source of the emissions, for example electricity, E as the cumulative emissions of the producers, and Y as the price of an emission allowance typically representing one ton of CO 2 equivalent.…”

Section: Introductionmentioning

confidence: 99%

“…Motivated by the analysis of mathematical models of the CO 2 emissions markets, see for example [3,18,2,4, 1], we are interested in the case of forward processes (X t = (P t , E t )) 0≤t≤T having a onedimensional component (E t ) 0≤t≤T with bounded variations, and a backward component (Y t ) 0≤t≤T having a terminal value given by a monotone function φ of E T , and especially when φ is an indicator function of the form φ = 1 [Λ,+∞) . In [1], we proposed an unrealistic toy example for which we showed that, while the terminal condition could not be enforced, it was still possible to prove existence and uniqueness of a solution provided parts of the terminal condition are allowed to become part of the solution.…”

Section: Introductionmentioning

confidence: 99%

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Singular FBSDEs and scalar conservation laws driven by diffusion processes

Carmona

Delarue²

2012

Probab. Theory Relat. Fields

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ABSTRACT. Motivated by earlier work on the use of fully-coupled Forward-Backward Stochastic Differential Equations (henceforth FBSDEs) in the analysis of mathematical models for the CO2 emissions markets, the present study is concerned with the analysis of these equations when the generator of the forward equation has a conservative degenerate structure and the terminal condition of the backward equation is a non-smooth function of the terminal value of the forward component. We show that a general form of existence and uniqueness result still holds. When the function giving the terminal condition is binary, we also show that the flow property of the forward component of the solution can fail at the terminal time. In particular, we prove that a Dirac point mass appears in its distribution, exactly at the location of the jump of the binary function giving the terminal condition. We provide a detailed analysis of the breakdown of the Markovian representation of the solution at the terminal time.

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On the Modeling of CO₂ EUA and CER Prices of EU‐ETS for the 2008–2012 Period

Gürler

Yenigün

Çaǧlar

et al. 2016

Appl Stoch Models Bus & Ind

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Increased consumption of fossil fuels in industrial production has led to a significant elevation in the emission of greenhouse gases and to global warming. The most effective international action against global warming is the Kyoto Protocol, which aims to reduce carbon emissions to desired levels in a certain time span. Carbon trading is one of the mechanisms used to achieve the desired reductions.

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Optimal Stochastic Control and Carbon Price Formation

Cited by 88 publications

References 7 publications

Explaining European Emission Allowance Price Dynamics: Evidence from Phase II

Explaining European Emission Allowance Price Dynamics: Evidence from Phase II

Singular FBSDEs and scalar conservation laws driven by diffusion processes

On the Modeling of CO₂ EUA and CER Prices of EU‐ETS for the 2008–2012 Period

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Optimal Stochastic Control and Carbon Price Formation

Cited by 88 publications

References 7 publications

Explaining European Emission Allowance Price Dynamics: Evidence from Phase II

Explaining European Emission Allowance Price Dynamics: Evidence from Phase II

Singular FBSDEs and scalar conservation laws driven by diffusion processes

On the Modeling of CO2 EUA and CER Prices of EU‐ETS for the 2008–2012 Period

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On the Modeling of CO₂ EUA and CER Prices of EU‐ETS for the 2008–2012 Period