Swing options in commodity markets: a multidimensional Lévy diffusion model

We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional Lévy process. We set up a valuation model in terms of a dynamic programming problem where the option can be e...

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Vydané v:	Mathematical methods of operations research (Heidelberg, Germany) Ročník 79; číslo 1; s. 31 - 67
Hlavní autori:	Eriksson, Marcus, Lempa, Jukka, Nilssen, Trygve Kastberg
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2014 Springer Nature B.V
Predmet:	Business and Management Calculus of Variations and Optimal Control; Optimization Commodities Commodity prices Dynamic programming Mathematical models Mathematics Mathematics and Statistics Operations research Operations Research/Decision Theory Original Article Securities prices Studies Valuation Multi-factor model Dynamic programming problem HJB-equation Lévy diffusion Swing option Flexible load contract Finite difference method
ISSN:	1432-2994, 1432-5217
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Abstract	We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional Lévy process. We set up a valuation model in terms of a dynamic programming problem where the option can be exercised continuously in time. Here, the number of swing rights is given by a total volume constraint. We analyze some general properties of the model and study the solution by analyzing the associated HJB-equation. Furthermore, we discuss the issues caused by the multi-dimensionality of the commodity price model. The results are illustrated numerically with three explicit examples.
AbstractList	We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional Lévy process. We set up a valuation model in terms of a dynamic programming problem where the option can be exercised continuously in time. Here, the number of swing rights is given by a total volume constraint. We analyze some general properties of the model and study the solution by analyzing the associated HJB-equation. Furthermore, we discuss the issues caused by the multi-dimensionality of the commodity price model. The results are illustrated numerically with three explicit examples. [PUBLICATION ABSTRACT] We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional Levy process. We set up a valuation model in terms of a dynamic programming problem where the option can be exercised continuously in time. Here, the number of swing rights is given by a total volume constraint. We analyze some general properties of the model and study the solution by analyzing the associated HJB-equation. Furthermore, we discuss the issues caused by the multi-dimensionality of the commodity price model. The results are illustrated numerically with three explicit examples. We study valuation of swing options on commodity markets when the commodity prices are driven by multiple factors. The factors are modeled as diffusion processes driven by a multidimensional Lévy process. We set up a valuation model in terms of a dynamic programming problem where the option can be exercised continuously in time. Here, the number of swing rights is given by a total volume constraint. We analyze some general properties of the model and study the solution by analyzing the associated HJB-equation. Furthermore, we discuss the issues caused by the multi-dimensionality of the commodity price model. The results are illustrated numerically with three explicit examples.
Author	Nilssen, Trygve Kastberg Eriksson, Marcus Lempa, Jukka
Author_xml	– sequence: 1 givenname: Marcus surname: Eriksson fullname: Eriksson, Marcus email: mkerikss@math.uio.no organization: Department of Mathematics, University of Oslo – sequence: 2 givenname: Jukka surname: Lempa fullname: Lempa, Jukka organization: Institute for Economics, Oslo and Akershus University College – sequence: 3 givenname: Trygve Kastberg surname: Nilssen fullname: Nilssen, Trygve Kastberg organization: Department of Economics and Business Administration, University of Agder
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References	WahabMIMYinZEdirisingheNCPPricing swing options in the electricity markets under regime-switching uncertaintyQuant Financ201010997599410.1080/146976809035478991210.911252738822 BurgerMGraeblerBSchindlmayrGManaging energy risk2007New YorkWiley Finance ApplebaumDLévy processes and stochastic calculus20092CambridgeCambridge University Press10.1017/CBO97805118097811200.60001 Deng S (2000) Stochastic models of energy commodity prices and their applications: mean-reversion with jumps and spikes. Power working paper 073, University of California Energy Institute DahlgrenMA continuous time model to price commodity based swing optionsRev Deriv Res200581274710.1007/s11147-005-1006-91134.914062122352 HaarbrückerGKuhnDValuation of electricity swing options by multistage stochastic programmingAutomatica20094588989910.1016/j.automatica.2008.11.0221177.90299 KieselRGernhardJStollS-OValuation of commodity based swing optionsJ Energy Mark20103391112 MarshallTJMark ReesorRForest of stochastic meshes: a new method for valuing high-dimensional swing optionsOper Res Lett201139172110.1016/j.orl.2010.11.0031208.911492748708 BenderCPrimal and dual pricing of multiple exercise options in continuous timeSIAM J Financ Math20112156258610.1137/09077076X1270.91090 JailletPRonnMTompadisSValuation of commodity based swing optionsManag Sci2004142223248 Lund A-C, Ollmar F (2003) Analyzing flexible load contracts (preprint) BenthFELempaJNilssenTKOn the optimal exercise of swing options in electricity marketsJ Energy Mark201244328 FlemingWHSonerMControlled Markov processes and viscosity solutions20062New YorkSpringer1105.60005 HamblyBHowisonSKlugeTModelling spikes and pricing swing options in electricity marketsQuant Financ20099893794910.1080/146976808025968561182.911762599022 KeppoJPricing of electricity swing contractsJ Deriv200411264310.3905/jod.2004.391033 KjaerMPricing of swing options in a mean reverting model with jumpsAppl Math Financ200815547950210.1080/135048608021705561156.913772489969 Edoli E, Fiorenzani S, Ravelli S, Vargiolu T (2012) Modeling and valuing make-up clauses in gas swing valuation. Energy Econ. doi:10.1016/j.eneco.2011.11.019 BenthFEKallsenJMeyer-BrandisTA non-Gaussian Ornstein–Uhlenbeck process for electricity spot price modeling and derivative pricingAppl Math Financ20071415316910.1080/135048606007250311160.913372323278 CarmonaRTouziNOptimal multiple stopping and valuation of swing optionsMath Financ200818223926810.1111/j.1467-9965.2007.00331.x1133.914992395575 BjorganRSongHLiuC-CDahlgrenRPricing flexible electrcity contractsIEEE Trans Electr Syst2000152477482 FE Benth (452_CR4) 2012; 4 G Haarbrücker (452_CR12) 2009; 45 M Burger (452_CR6) 2007 M Kjaer (452_CR17) 2008; 15 MIM Wahab (452_CR20) 2010; 10 452_CR10 J Keppo (452_CR15) 2004; 11 B Hambly (452_CR13) 2009; 9 P Jaillet (452_CR14) 2004; 14 FE Benth (452_CR3) 2007; 14 M Dahlgren (452_CR8) 2005; 8 WH Fleming (452_CR11) 2006 452_CR18 R Kiesel (452_CR16) 2010; 3 R Carmona (452_CR7) 2008; 18 D Applebaum (452_CR1) 2009 C Bender (452_CR2) 2011; 2 452_CR9 R Bjorgan (452_CR5) 2000; 15 TJ Marshall (452_CR19) 2011; 39
References_xml	– reference: FlemingWHSonerMControlled Markov processes and viscosity solutions20062New YorkSpringer1105.60005 – reference: BurgerMGraeblerBSchindlmayrGManaging energy risk2007New YorkWiley Finance – reference: HaarbrückerGKuhnDValuation of electricity swing options by multistage stochastic programmingAutomatica20094588989910.1016/j.automatica.2008.11.0221177.90299 – reference: DahlgrenMA continuous time model to price commodity based swing optionsRev Deriv Res200581274710.1007/s11147-005-1006-91134.914062122352 – reference: BenthFELempaJNilssenTKOn the optimal exercise of swing options in electricity marketsJ Energy Mark201244328 – reference: KjaerMPricing of swing options in a mean reverting model with jumpsAppl Math Financ200815547950210.1080/135048608021705561156.913772489969 – reference: Edoli E, Fiorenzani S, Ravelli S, Vargiolu T (2012) Modeling and valuing make-up clauses in gas swing valuation. Energy Econ. doi:10.1016/j.eneco.2011.11.019 – reference: Lund A-C, Ollmar F (2003) Analyzing flexible load contracts (preprint) – reference: ApplebaumDLévy processes and stochastic calculus20092CambridgeCambridge University Press10.1017/CBO97805118097811200.60001 – reference: JailletPRonnMTompadisSValuation of commodity based swing optionsManag Sci2004142223248 – reference: MarshallTJMark ReesorRForest of stochastic meshes: a new method for valuing high-dimensional swing optionsOper Res Lett201139172110.1016/j.orl.2010.11.0031208.911492748708 – reference: KieselRGernhardJStollS-OValuation of commodity based swing optionsJ Energy Mark20103391112 – reference: BjorganRSongHLiuC-CDahlgrenRPricing flexible electrcity contractsIEEE Trans Electr Syst2000152477482 – reference: HamblyBHowisonSKlugeTModelling spikes and pricing swing options in electricity marketsQuant Financ20099893794910.1080/146976808025968561182.911762599022 – reference: BenthFEKallsenJMeyer-BrandisTA non-Gaussian Ornstein–Uhlenbeck process for electricity spot price modeling and derivative pricingAppl Math Financ20071415316910.1080/135048606007250311160.913372323278 – reference: Deng S (2000) Stochastic models of energy commodity prices and their applications: mean-reversion with jumps and spikes. Power working paper 073, University of California Energy Institute – reference: WahabMIMYinZEdirisingheNCPPricing swing options in the electricity markets under regime-switching uncertaintyQuant Financ201010997599410.1080/146976809035478991210.911252738822 – reference: BenderCPrimal and dual pricing of multiple exercise options in continuous timeSIAM J Financ Math20112156258610.1137/09077076X1270.91090 – reference: CarmonaRTouziNOptimal multiple stopping and valuation of swing optionsMath Financ200818223926810.1111/j.1467-9965.2007.00331.x1133.914992395575 – reference: KeppoJPricing of electricity swing contractsJ Deriv200411264310.3905/jod.2004.391033 – volume: 14 start-page: 153 year: 2007 ident: 452_CR3 publication-title: Appl Math Financ doi: 10.1080/13504860600725031 – ident: 452_CR9 – volume: 15 start-page: 477 issue: 2 year: 2000 ident: 452_CR5 publication-title: IEEE Trans Electr Syst – volume-title: Lévy processes and stochastic calculus year: 2009 ident: 452_CR1 doi: 10.1017/CBO9780511809781 – volume: 2 start-page: 562 issue: 1 year: 2011 ident: 452_CR2 publication-title: SIAM J Financ Math doi: 10.1137/09077076X – ident: 452_CR10 doi: 10.1016/j.eneco.2011.11.019 – volume: 15 start-page: 479 issue: 5 year: 2008 ident: 452_CR17 publication-title: Appl Math Financ doi: 10.1080/13504860802170556 – volume: 14 start-page: 223 issue: 2 year: 2004 ident: 452_CR14 publication-title: Manag Sci – ident: 452_CR18 – volume: 45 start-page: 889 year: 2009 ident: 452_CR12 publication-title: Automatica doi: 10.1016/j.automatica.2008.11.022 – volume: 39 start-page: 17 year: 2011 ident: 452_CR19 publication-title: Oper Res Lett doi: 10.1016/j.orl.2010.11.003 – volume: 9 start-page: 937 issue: 8 year: 2009 ident: 452_CR13 publication-title: Quant Financ doi: 10.1080/14697680802596856 – volume: 10 start-page: 975 issue: 9 year: 2010 ident: 452_CR20 publication-title: Quant Financ doi: 10.1080/14697680903547899 – volume: 4 start-page: 3 issue: 4 year: 2012 ident: 452_CR4 publication-title: J Energy Mark doi: 10.21314/JEM.2011.065 – volume: 3 start-page: 91 issue: 3 year: 2010 ident: 452_CR16 publication-title: J Energy Mark doi: 10.21314/JEM.2010.045 – volume: 8 start-page: 27 issue: 1 year: 2005 ident: 452_CR8 publication-title: Rev Deriv Res doi: 10.1007/s11147-005-1006-9 – volume-title: Managing energy risk year: 2007 ident: 452_CR6 – volume: 11 start-page: 26 year: 2004 ident: 452_CR15 publication-title: J Deriv doi: 10.3905/jod.2004.391033 – volume-title: Controlled Markov processes and viscosity solutions year: 2006 ident: 452_CR11 – volume: 18 start-page: 239 issue: 2 year: 2008 ident: 452_CR7 publication-title: Math Financ doi: 10.1111/j.1467-9965.2007.00331.x
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SubjectTerms	Business and Management Calculus of Variations and Optimal Control; Optimization Commodities Commodity prices Dynamic programming Mathematical models Mathematics Mathematics and Statistics Operations research Operations Research/Decision Theory Original Article Securities prices Studies Valuation
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Title	Swing options in commodity markets: a multidimensional Lévy diffusion model
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