Skip to main content
Top
Published in: Mathematics and Financial Economics 3/2021

11-01-2021 | Original Paper

Forward price and fitting of electricity Nord Pool market under regime-switching two-factor model

Authors: Farshid Mehrdoust, Idin Noorani

Published in: Mathematics and Financial Economics | Issue 3/2021

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Jump in electricity prices is often due to shock in electricity demand or shock in existing electricity supplies, which can be caused by sudden changes in temperature or production and system failure. Since jumps in electricity dynamics are directly related to the regime switch, we model them via the chain itself and consider a regime switching model for electricity spot price dynamic. Next, we determine an equivalent measure by Esscher transform and through it we evaluate the electricity forwards and risk premium. We apply expectation maximization algorithm to estimate parameters of the model. Furthermore, we use the real data of Nord Pool market to calibration of the proposed model. Using the characteristic function of model, we obtain a closed-form for forward contracts of Nord Pool market. Finally, we provide forward surfaces which show the months, quarters and seasons-ahead prices.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Fink, G.A.: Markov Models for Pattern Recognition, From Theory to Applications. Springer, Berlin (2008)MATH Fink, G.A.: Markov Models for Pattern Recognition, From Theory to Applications. Springer, Berlin (2008)MATH
2.
go back to reference Hahn, M., Fruhwirth-Schnatter, S., Sass, J.: Estimating models based on Markov jump processes given fragmented observation series. AStA Adv. Stat. Anal. 93(4), 403–425 (2009)MathSciNetMATHCrossRef Hahn, M., Fruhwirth-Schnatter, S., Sass, J.: Estimating models based on Markov jump processes given fragmented observation series. AStA Adv. Stat. Anal. 93(4), 403–425 (2009)MathSciNetMATHCrossRef
3.
go back to reference Hamilton, J.: Regime Switching Models, The New Palgrave Dictionary of Economics, 2nd edn (2008) Hamilton, J.: Regime Switching Models, The New Palgrave Dictionary of Economics, 2nd edn (2008)
5.
go back to reference Mehrdoust, F., Noorani, I.: Pricing S & P500 barrier put option of American type under Heston-CIR model with regime-switching. Int. J. Financial Eng. 6(2), 1–17 (2019)MathSciNetCrossRef Mehrdoust, F., Noorani, I.: Pricing S & P500 barrier put option of American type under Heston-CIR model with regime-switching. Int. J. Financial Eng. 6(2), 1–17 (2019)MathSciNetCrossRef
6.
go back to reference Goutte, S., Ismail, A., Pham, H.: Regime-switching stochastic volatility model: estimation and calibration to VIX options. Appl. Math. Finance 24(1), 38–75 (2017)MathSciNetMATHCrossRef Goutte, S., Ismail, A., Pham, H.: Regime-switching stochastic volatility model: estimation and calibration to VIX options. Appl. Math. Finance 24(1), 38–75 (2017)MathSciNetMATHCrossRef
7.
go back to reference Benth, F.E., Benth, J.S., Koekebakker, S.: Stochastic Modeling of Electricity and Related Markets. World Scientific, Singapore (2008)MATHCrossRef Benth, F.E., Benth, J.S., Koekebakker, S.: Stochastic Modeling of Electricity and Related Markets. World Scientific, Singapore (2008)MATHCrossRef
8.
go back to reference Janczura, J., Weron, R.: Efficient estimation of Markov regime-switching models: an application to electricity spot prices. AStA Adv. Stat. Anal. 96, 385–407 (2012)MathSciNetMATHCrossRef Janczura, J., Weron, R.: Efficient estimation of Markov regime-switching models: an application to electricity spot prices. AStA Adv. Stat. Anal. 96, 385–407 (2012)MathSciNetMATHCrossRef
9.
go back to reference Mount, T.D., Ning, Y., Cai, X.: Predicting price spikes in electricity markets using a regime-switching model with time-varying parameters. Energy Econ. 28(11), 62–80 (2006)CrossRef Mount, T.D., Ning, Y., Cai, X.: Predicting price spikes in electricity markets using a regime-switching model with time-varying parameters. Energy Econ. 28(11), 62–80 (2006)CrossRef
10.
go back to reference Mari, C.: Regime-switching characterization of electricity prices dynamics. Phys. A Stat. Mech. Appl. 371(2), 552–564 (2006)CrossRef Mari, C.: Regime-switching characterization of electricity prices dynamics. Phys. A Stat. Mech. Appl. 371(2), 552–564 (2006)CrossRef
11.
go back to reference Bierbrauer, M., Truck, S., Weron, R.: Modeling electricity prices with regime-switching models. Int. Conf. Comput. Sci. 3039, 859–867 (2004)MATH Bierbrauer, M., Truck, S., Weron, R.: Modeling electricity prices with regime-switching models. Int. Conf. Comput. Sci. 3039, 859–867 (2004)MATH
12.
go back to reference Huisman, R., Mahieu, R.: Regime jumps in electricity prices. Energy Econ. 25(5), 425–434 (2003)CrossRef Huisman, R., Mahieu, R.: Regime jumps in electricity prices. Energy Econ. 25(5), 425–434 (2003)CrossRef
13.
go back to reference Werona, R., Bierbrauerb, M., Truck, S.: Modeling electricity prices: jump diffusion and regime switching. Phys. A Stat. Mech. Appl. 336(1–2), 39–48 (2004)CrossRef Werona, R., Bierbrauerb, M., Truck, S.: Modeling electricity prices: jump diffusion and regime switching. Phys. A Stat. Mech. Appl. 336(1–2), 39–48 (2004)CrossRef
14.
go back to reference Pircalabu, A., Benth, F.E.: A regime-switching copula approach to modeling day-ahead prices in coupled electricity markets. Energy Econ. 68, 283–302 (2017)CrossRef Pircalabu, A., Benth, F.E.: A regime-switching copula approach to modeling day-ahead prices in coupled electricity markets. Energy Econ. 68, 283–302 (2017)CrossRef
15.
go back to reference Janczura, J., Weron, R.: Inference for Markov regime-switching models of electricity spot prices. In: Quantitative Energy Finance. Springer, New York, NY, pp. 137–155 (2014) Janczura, J., Weron, R.: Inference for Markov regime-switching models of electricity spot prices. In: Quantitative Energy Finance. Springer, New York, NY, pp. 137–155 (2014)
16.
go back to reference Paraschiv, F., Fleten, S.E., Schürle, M.: A spot-forward model for electricity prices with regime shifts. Energy Econ. 47, 142–153 (2015)CrossRef Paraschiv, F., Fleten, S.E., Schürle, M.: A spot-forward model for electricity prices with regime shifts. Energy Econ. 47, 142–153 (2015)CrossRef
17.
go back to reference Botterud, A., Kristiansen, T., Ilic, M.D.: The relationship between spot and futures prices in the Nord Pool electricity market. Energy Econ. 32(5), 967–978 (2010)CrossRef Botterud, A., Kristiansen, T., Ilic, M.D.: The relationship between spot and futures prices in the Nord Pool electricity market. Energy Econ. 32(5), 967–978 (2010)CrossRef
18.
go back to reference Weron, R.: Market price of risk implied by Asian-style electricity options and futures. Energy Econ. 30(3), 1098–1115 (2008)CrossRef Weron, R.: Market price of risk implied by Asian-style electricity options and futures. Energy Econ. 30(3), 1098–1115 (2008)CrossRef
19.
go back to reference Carmona, R., Coulon, M., Schwarz, D.: Electricity price modeling and asset valuation: a multi-fuel structural approach. Math. Financial Econ. 7(2), 167–202 (2013)MathSciNetMATHCrossRef Carmona, R., Coulon, M., Schwarz, D.: Electricity price modeling and asset valuation: a multi-fuel structural approach. Math. Financial Econ. 7(2), 167–202 (2013)MathSciNetMATHCrossRef
20.
go back to reference Hambly, B., Howison, S., Kluge, T.: Modelling spikes and pricing swing options in electricity markets. Quant. Finance 9(8), 937–949 (2007)MathSciNetMATHCrossRef Hambly, B., Howison, S., Kluge, T.: Modelling spikes and pricing swing options in electricity markets. Quant. Finance 9(8), 937–949 (2007)MathSciNetMATHCrossRef
21.
go back to reference Cartea, A., Figueroa, M.G.: Pricing in electricity markets: a mean reverting jump diffusion model with seasonality. Appl. Math. Finance 12(4), 313–335 (2005)MATHCrossRef Cartea, A., Figueroa, M.G.: Pricing in electricity markets: a mean reverting jump diffusion model with seasonality. Appl. Math. Finance 12(4), 313–335 (2005)MATHCrossRef
22.
go back to reference Kiesel, R., Schindlmayr, G., Boerger, R.H.: A two-factor model for the electricity forward market. Quant. Finance 9(3), 279–287 (2009)MathSciNetMATHCrossRef Kiesel, R., Schindlmayr, G., Boerger, R.H.: A two-factor model for the electricity forward market. Quant. Finance 9(3), 279–287 (2009)MathSciNetMATHCrossRef
23.
go back to reference 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)MathSciNetMATHCrossRef 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)MathSciNetMATHCrossRef
24.
go back to reference Wimschulte, J.: The futures and forward price differential in the Nordic electricity market. Energy Policy 38(8), 4731–4733 (2010)CrossRef Wimschulte, J.: The futures and forward price differential in the Nordic electricity market. Energy Policy 38(8), 4731–4733 (2010)CrossRef
25.
go back to reference Benth, F.E., Nunno, G.D., Khedher, A.: Computation of greeks in multi-factor models with applications to power and commodity markets. J. Energy Mark. 5(4), 3–31 (2010)CrossRef Benth, F.E., Nunno, G.D., Khedher, A.: Computation of greeks in multi-factor models with applications to power and commodity markets. J. Energy Mark. 5(4), 3–31 (2010)CrossRef
26.
go back to reference Schwartz, S.E., Smith, J.E.: Short-term variations and long-term dynamics in commodity prices. Manag. Sci. 46(7), 893–911 (2000)CrossRef Schwartz, S.E., Smith, J.E.: Short-term variations and long-term dynamics in commodity prices. Manag. Sci. 46(7), 893–911 (2000)CrossRef
27.
go back to reference Benth, F.E., Ortiz-Latorre, S.: A pricing measure to explain the risk premium in power markets. SIAM J. Financial Math. 5(1), 685–728 (2014)MathSciNetMATHCrossRef Benth, F.E., Ortiz-Latorre, S.: A pricing measure to explain the risk premium in power markets. SIAM J. Financial Math. 5(1), 685–728 (2014)MathSciNetMATHCrossRef
28.
29.
go back to reference Geman, H.: Commodities and Commodity Derivatives. Wiley, Hoboken (2005) Geman, H.: Commodities and Commodity Derivatives. Wiley, Hoboken (2005)
30.
go back to reference René, A., Campi, L., Langrené, N.: A structural risk-neutral model for pricing and hedging power derivatives. Math. Finance 23(3), 387–438 (2013)MathSciNetMATHCrossRef René, A., Campi, L., Langrené, N.: A structural risk-neutral model for pricing and hedging power derivatives. Math. Finance 23(3), 387–438 (2013)MathSciNetMATHCrossRef
31.
go back to reference Elliott, R.J., Chan, L., Siu, T.K.: Option pricing and Esscher transform under regime switching. Ann. Finance 1(2), 423–432 (2005)MATHCrossRef Elliott, R.J., Chan, L., Siu, T.K.: Option pricing and Esscher transform under regime switching. Ann. Finance 1(2), 423–432 (2005)MATHCrossRef
32.
go back to reference Elliott, R., Aggoun, L., Moore, J.B.: Hidden Markov Models: Estimation and Control, Finance and Stochastics, vol. 29. Springer, Berlin (1995)MATH Elliott, R., Aggoun, L., Moore, J.B.: Hidden Markov Models: Estimation and Control, Finance and Stochastics, vol. 29. Springer, Berlin (1995)MATH
33.
go back to reference Benth, F.E., Schmeck, M.D.: Pricing futures and options in electricity markets. In: The Interrelationship Between Financial and Energy Markets. Springer, Berlin, pp. 233–260 (2014) Benth, F.E., Schmeck, M.D.: Pricing futures and options in electricity markets. In: The Interrelationship Between Financial and Energy Markets. Springer, Berlin, pp. 233–260 (2014)
34.
35.
go back to reference Shen, Y., Fan, K., Siu, T.K.: Option valuation under a double regime-switching model. J. Futures Mark. 34(5), 451–478 (2014)CrossRef Shen, Y., Fan, K., Siu, T.K.: Option valuation under a double regime-switching model. J. Futures Mark. 34(5), 451–478 (2014)CrossRef
36.
go back to reference Turkvatan, A., Hayfavi, A., Omay, T.: A regime switching model for temperature modeling and applications to weather derivatives pricing. Math. Financial Econ. 14(1), 1–42 (2020)MathSciNetMATHCrossRef Turkvatan, A., Hayfavi, A., Omay, T.: A regime switching model for temperature modeling and applications to weather derivatives pricing. Math. Financial Econ. 14(1), 1–42 (2020)MathSciNetMATHCrossRef
37.
go back to reference Raphson, J.: Analysis aequationum universalis. J. Book R. Soc. Lond. (1690) Raphson, J.: Analysis aequationum universalis. J. Book R. Soc. Lond. (1690)
38.
go back to reference Amrein, M., Wihler, T.P.: An adaptive Newton-method based on a dynamical systems approach. Commun. Nonlinear Sci. Numer. Simul. 19(9), 2958–2973 (2014)MathSciNetMATHCrossRef Amrein, M., Wihler, T.P.: An adaptive Newton-method based on a dynamical systems approach. Commun. Nonlinear Sci. Numer. Simul. 19(9), 2958–2973 (2014)MathSciNetMATHCrossRef
39.
go back to reference Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. 39(1), 1–22 (1977)MathSciNetMATH Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. 39(1), 1–22 (1977)MathSciNetMATH
42.
go back to reference Lucia, J.J., Schwartz, S.E.: Electricity prices and power derivatives: evidence from the Nordic power exchange. Rev. Deriv. Res. 5(1), 5–50 (2002)MATHCrossRef Lucia, J.J., Schwartz, S.E.: Electricity prices and power derivatives: evidence from the Nordic power exchange. Rev. Deriv. Res. 5(1), 5–50 (2002)MATHCrossRef
44.
go back to reference Geman, H., Vasicek, O.: Forward and futures contracts on non-storable commodities: the case of electricity. Risk 14(8), 93–97 (2001) Geman, H., Vasicek, O.: Forward and futures contracts on non-storable commodities: the case of electricity. Risk 14(8), 93–97 (2001)
45.
go back to reference Longstaff, F.A., Wang, A.W.: Electricity forward prices: a high-frequency empirical analysis. J. Finance 59(4), 1877–1900 (2004)CrossRef Longstaff, F.A., Wang, A.W.: Electricity forward prices: a high-frequency empirical analysis. J. Finance 59(4), 1877–1900 (2004)CrossRef
46.
go back to reference Diko, P., Lawford, S., Limpens, V.: Risk premia in electricity forward prices. Stud. Nonlinear Dyn. Econom. 10(3), 7 (2006)MATH Diko, P., Lawford, S., Limpens, V.: Risk premia in electricity forward prices. Stud. Nonlinear Dyn. Econom. 10(3), 7 (2006)MATH
47.
go back to reference Lucia, J.J., Torrò, H.: Short-term electricity futures prices: evidence on the time-varying risk premium. Available at SSRN 1014035 (2008) Lucia, J.J., Torrò, H.: Short-term electricity futures prices: evidence on the time-varying risk premium. Available at SSRN 1014035 (2008)
Metadata
Title
Forward price and fitting of electricity Nord Pool market under regime-switching two-factor model
Authors
Farshid Mehrdoust
Idin Noorani
Publication date
11-01-2021
Publisher
Springer Berlin Heidelberg
Published in
Mathematics and Financial Economics / Issue 3/2021
Print ISSN: 1862-9679
Electronic ISSN: 1862-9660
DOI
https://doi.org/10.1007/s11579-020-00287-6

Other articles of this Issue 3/2021

Mathematics and Financial Economics 3/2021 Go to the issue