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

Alexander, C.: Correlation and cointegration in energy markets. Managing Energy Price Risk, Risk Publications London, 2 edn, pp. 291–304 (1999)

Benth, F.E.: Cointegrated commodity markets and pricing of derivatives in a non-Gaussian framework. In: Advanced Modelling in Mathematical Finance. Springer Proceedings in Mathematics and Statistics, vol. 189. Springer, Cham, pp. 477–496 (2016)

Benth, F.E., Cartea, Á., Kiesel, R.: Pricing forward contracts in power markets by the certainty equivalence principle: explaining the sign of the market risk premium. J. Bank. Finance 32(10), 2006–2021 (2008)

Benth, F.E., Kallsen, J., Meyer-Brandis, T.: A non-Gaussian Ornstein–Uhlenbeck process for electricity spot price modeling and derivatives pricing. Appl. Math. Finance 14(2), 153–169 (2007)

Benth, F.E., Koekebakker, S.: Stochastic modeling of financial electricity contracts. Energy Econ. 30(3), 1116–1157 (2008)

Benth, F.E., Ortiz-Latorre, S.: A pricing measure to explain the risk premium in power markets. SIAM J. Financ. Math. 5(1), 685–728 (2014)

Benth, F.E., Šaltytė Benth, J.: Modeling and Pricing in Financial Markets for Weather Derivatives. World Scientific Publishing, Singapore (2012)

Benth, F.E., Sgarra, C.: The risk premium and the Esscher transform in power markets. Stoch. Anal. Appl. 30(1), 20–43 (2012)

Benth, F.E., Šaltytė Benth, J., Koekebakker, S.: Stochastic Modelling of Electricity and Related Markets. Advanced Series on Statistical Science & Applied Probability, vol. 11. World Scientific Publishing, Hackensack (2008)

Bessembinder, H., Lemmon, M.L.: Equilibrium pricing and optimal hedging in electricity forward markets. J. Finance 57(3), 1347–1382 (2002)

Bjerksund, P., Rasmussen, H., Stensland, G.: Valuation and risk management in the Norwegian electricity market. Energy, Natural Resources and Environmental Economics. Springer, pp. 167–185 (2010)

Blanes, S., Casas, F., Oteo, J.A., Ros, J.: The magnus expansion and some of its applications. Phys. Rep. 470(5), 151–238 (2009)

Brockwell, P.J., Schlemm, E.: Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations. J. Multivar. Anal. 115, 217–251 (2013)

Broszkiewicz-Suwaj, E., Weron, A.: Calibration of the multi-factor HJM model for energy market. Acta Phys. Pol. B 37, 1455 (2006)

Cartea, Á., Figueroa, M.G.: Pricing in electricity markets: a mean reverting jump diffusion model with seasonality. Appl. Math. Finance 12(4), 313–335 (2005)

Cartea, Á., Williams, T.: UK gas markets: the market price of risk and applications to multiple interruptible supply contracts. Energy Econ. 30(3), 829–846 (2008)

Clewlow, L., Strickland, C.: Valuing energy options in a one factor model fitted to forward prices. Research Paper Series 10. Quantitative Finance Research Centre, University of Technology, Sydney (1999)

Cohen, S.N., Elliott, R.J.: Stochastic Calculus and Applications. Probability and Its Applications, 2nd edn. Springer, New York (2015)

Cont, R., Tankov, P.: Financial Modelling with Jump Processes. Chapman & Hall/CRC Financial Mathematics Series. Chapman & Hall, Boca Raton (2004)

De Jong, C., Schneider, S.: Cointegration between gas and power spot prices. J. Energy Mark. 2(3), 27–46 (2009)

Edoli, E., Gallana, M., Vargiolu, T.: Optimal intra-day power trading with a Gaussian additive process. J. Energy Mark. 10(4), 23–42 (2017)

Fanone, E., Gamba, A., Prokopczuk, M.: The case of negative day-ahead electricity prices. Energy Econ. 35(C), 22–34 (2013)

Farkas, W., Gourier, E., Huitema, R., Necula, C.: A two-factor cointegrated commodity price model with an application to spread option pricing. J. Bank. Finance 77, 249–268 (2017)

Geman, H.: Commodities and Commodity Derivatives. Modeling and Pricing for Agriculturals, Metals and Energy, HAL (2005)

Geman, H., Roncoroni, A.: Understanding the fine structure of electricity prices. J. Bus. 79(3), 1225–1262 (2006)

Heath, D., Jarrow, R., Morton, A.: Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation. Econometrica 60(1), 77–105 (1992)

Hinderks, W., Wagner, A., Korn, R.: A structural Heath–Jarrow–Morton framework for consistent intraday, spot, and futures electricity prices. Technical report. arXiv:1803.08831 (2018)

Hinz, J., von Grafenstein, L., Verschuere, M., Wilhelm, M.: Pricing electricity risk by interest rate methods. Quant. Finance 5(1), 49–60 (2005)

Jaimungal, S., Surkov, V.: Lévy-based cross-commodity models and derivative valuation. SIAM J. Financ. Math. 2(1), 464–487 (2011)

Jiao, Y., Ma, C., Scotti, S., Sgarra, C.: A branching process approach to power markets. Energy Econ. (2018). https://doi.org/10.1016/j.eneco.2018.03.002

Kallsen, J., Shiryaev, A.N.: The cumulant process and Esscher’s change of measure. Finance Stoch. 6(4), 397–428 (2002)

Karatzas, I., Shreve, S.E.: Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics, vol. 113, 2nd edn. Springer, New York (1991)

Kiesel, R., Paraschiv, F.: Econometric analysis of 15-minute intraday electricity prices. Energy Econ. 64, 77–90 (2017)

Kiesel, R., Schindlmayr, G., Börger, R.H.: A two-factor model for the electricity forward market. Quant. Finance 9(3), 279–287 (2009)

Koekebakker, S.: An arithmetic forward curve model for the electricity market. Working Paper 2003:5, Agder University College, Norway (2003)

Kolos, S.P., Ronn, E.I.: Estimating the commodity market price of risk for energy prices. Energy Econ. 30(2), 621–641 (2008)

Latini, L., Piccirilli, M., Vargiolu, T.: Mean-reverting no-arbitrage additive models for forward curves in energy markets. Energy Econ. (2018). https://doi.org/10.1016/j.eneco.2018.03.001

Lépingle, D., Mémin, J.: Sur l’intégrabilité uniforme des martingales exponentielles. Z. Wahrsch. Verw. Geb. 42(3), 175–203 (1978)

Lucia, J.J., Schwartz, E.S.: Electricity prices and power derivatives: evidence from the nordic power exchange. Rev. Deriv. Res. 5(1), 5–50 (2002)

Musiela, M., Rutkowski, M.: Martingale Methods in Financial Modelling. Applications of Mathematics, vol. 36. Springer, Berlin (1997)

Novikov, A.A.: A certain identity for stochastic integrals. Teor. Verojatnost. i Primenen. 17, 761–765 (1972)

Øksendal, B., Sulem, A.: Applied Stochastic Control of Jump Diffusions. Universitext, 2nd edn. Springer, Berlin (2007)

Paschke, R., Prokopczuk, M.: Integrating multiple commodities in a model of stochastic price dynamics. J. Energy Mark. 2(3), 47–82 (2009)

Piccirilli, M., Schmeck, M.D., Vargiolu, T.: Capturing the power options smile by an additive two-factor model for futures prices. Technical report (2018)

Privault, N.: Combinatorics of Poisson Stochastic Integrals with Random Integrands. Stochastic Analysis for Poisson Point Processes: Malliavin Calculus, Wiener-Itô Chaos Expansions and Stochastic Geometry, pp. 37–80. Springer, Cham (2016)

Protter, P.E.: Stochastic Integration and Differential Equations. Applications of Mathematics. Stochastic Modelling and Applied Probability, vol. 21, 2nd edn. Springer, Berlin (2004)

Riordan, J.: Moment recurrence relations for binomial, Poisson and hypergeometric frequency distributions. Ann. Math. Stat. 8(2), 103–111 (1937)

Serletis, A.: Quantitative and Empirical Analysis of Energy Markets. World Scientific Publishing, Singapore (2012)

Weron, R.: Market price of risk implied by Asian-style electricity options and futures. Energy Econ. 30(3), 1098–1115 (2008)