Estimation of Lévy-driven Ornstein–Uhlenbeck processes: application to modeling of CO2 and fuel-switching
This paper proposes an estimation methodology for Lévy-driven Ornstein–Uhlenbeck processes. The estimation unfolds in two steps, with a least-squares method for a subset of parameters in the first stage, and a constrained maximum likelihood for the remaining diffusion and Lévy distribution parameter...
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| Veröffentlicht in: | Annals of operations research 2017-08, Vol.255 (1-2), p.169-197 |
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| creator | Chevallier, Julien Goutte, Stéphane |
| description | This paper proposes an estimation methodology for Lévy-driven Ornstein–Uhlenbeck processes. The estimation unfolds in two steps, with a least-squares method for a subset of parameters in the first stage, and a constrained maximum likelihood for the remaining diffusion and Lévy distribution parameters. We develop this estimation procedure to demonstrate that the class of mean-reverting Lévy jump processes provides a better fit of the electricity and
CO
2
(carbon) market prices. In particular, we describe the dynamics of the fuel-switching price (from coal to gas) when taking into account carbon costs. Several stochastic processes are considered to model the fuel-switching price: (1) the Brownian motion, and (2) Poisson and a panel of Lévy jump processes. The results unambiguously point out the need to resort to jump modeling techniques to model satisfactorily the fuel-switching price. The Gaussianity assumption is also clearly rejected in favor of jump models, especially for pure-jump processes such as Lévy processes. |
| doi_str_mv | 10.1007/s10479-015-1967-5 |
| format | Article |
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CO
2
(carbon) market prices. In particular, we describe the dynamics of the fuel-switching price (from coal to gas) when taking into account carbon costs. Several stochastic processes are considered to model the fuel-switching price: (1) the Brownian motion, and (2) Poisson and a panel of Lévy jump processes. The results unambiguously point out the need to resort to jump modeling techniques to model satisfactorily the fuel-switching price. The Gaussianity assumption is also clearly rejected in favor of jump models, especially for pure-jump processes such as Lévy processes.</description><identifier>ISSN: 0254-5330</identifier><identifier>EISSN: 1572-9338</identifier><identifier>DOI: 10.1007/s10479-015-1967-5</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Brownian motion ; Business and Management ; Carbon dioxide ; Combinatorics ; Electricity pricing ; Estimating techniques ; Fuels ; Mathematical models ; Modelling ; Operations research ; Operations Research/Decision Theory ; Parameter estimation ; Stochastic processes ; Switching ; Theory of Computation</subject><ispartof>Annals of operations research, 2017-08, Vol.255 (1-2), p.169-197</ispartof><rights>Springer Science+Business Media New York 2015</rights><rights>Annals of Operations Research is a copyright of Springer, 2017.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p715-d64917980ed296e9c07f8a44a25556ed8143983254f25c3f3866d19d80e8ee223</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10479-015-1967-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10479-015-1967-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Chevallier, Julien</creatorcontrib><creatorcontrib>Goutte, Stéphane</creatorcontrib><title>Estimation of Lévy-driven Ornstein–Uhlenbeck processes: application to modeling of CO2 and fuel-switching</title><title>Annals of operations research</title><addtitle>Ann Oper Res</addtitle><description>This paper proposes an estimation methodology for Lévy-driven Ornstein–Uhlenbeck processes. The estimation unfolds in two steps, with a least-squares method for a subset of parameters in the first stage, and a constrained maximum likelihood for the remaining diffusion and Lévy distribution parameters. We develop this estimation procedure to demonstrate that the class of mean-reverting Lévy jump processes provides a better fit of the electricity and
CO
2
(carbon) market prices. In particular, we describe the dynamics of the fuel-switching price (from coal to gas) when taking into account carbon costs. Several stochastic processes are considered to model the fuel-switching price: (1) the Brownian motion, and (2) Poisson and a panel of Lévy jump processes. The results unambiguously point out the need to resort to jump modeling techniques to model satisfactorily the fuel-switching price. 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The estimation unfolds in two steps, with a least-squares method for a subset of parameters in the first stage, and a constrained maximum likelihood for the remaining diffusion and Lévy distribution parameters. We develop this estimation procedure to demonstrate that the class of mean-reverting Lévy jump processes provides a better fit of the electricity and
CO
2
(carbon) market prices. In particular, we describe the dynamics of the fuel-switching price (from coal to gas) when taking into account carbon costs. Several stochastic processes are considered to model the fuel-switching price: (1) the Brownian motion, and (2) Poisson and a panel of Lévy jump processes. The results unambiguously point out the need to resort to jump modeling techniques to model satisfactorily the fuel-switching price. The Gaussianity assumption is also clearly rejected in favor of jump models, especially for pure-jump processes such as Lévy processes.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10479-015-1967-5</doi><tpages>29</tpages></addata></record> |
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| subjects | Brownian motion Business and Management Carbon dioxide Combinatorics Electricity pricing Estimating techniques Fuels Mathematical models Modelling Operations research Operations Research/Decision Theory Parameter estimation Stochastic processes Switching Theory of Computation |
| title | Estimation of Lévy-driven Ornstein–Uhlenbeck processes: application to modeling of CO2 and fuel-switching |
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