Skip to main content
SpringerLink
Log in

Forward contract prices of electricity Nord Pool market: calibration and jump approximation

  • Published:
Sādhanā Aims and scope Submit manuscript

Abstract

This paper focuses on the forward contract price under a mean-reverting jump-diffusion electricity model and the Grandell idea. Based on historical spot prices from the electricity Nord Pool market, model parameters are calibrated under different conditions. First, we remove the jump data and calibrate the seasonal model parameters using least squares and Newton–Raphson methods. Then, the jump and the other parameters are obtained by the MLE method. Moreover, the first passage time is derived as a probability function and used it as an appropriate tool to know the behavior of the electricity spot price. Ultimately, months and quarters ahead forward data are achieved by the forward contract formula.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5

Similar content being viewed by others

Abbreviations

MLE:

Maximum likelihood estimation

HJB:

Hamilton Jacobi Bellman

NR:

Newton Raphson

References

  1. Schwartz E S 1997 The stochastic behavior of commodity prices: Implications for valuation and hedging. The Journal of finance. 52(3): 923–973

    Article  Google Scholar 

  2. Schwartz E and Smith J E 2000 Short-term variations and long-term dynamics in commodity prices. Management Science. 46(7): 893–911

    Article  Google Scholar 

  3. Lucia J J and Schwartz E S 2002 Electricity prices and power derivatives: Evidence from the nordic power exchange. Review of derivatives research. 5(1): 5–50

    Article  MATH  Google Scholar 

  4. Benth F E, Ekeland L, Hauge R and Nielsen B R F 2003 A note on arbitrage-free pricing of forward contracts in energy markets. Applied Mathematical Finance. 10(4): 325–336

    Article  MATH  Google Scholar 

  5. Bierbrauer M, Trück S and Weron R 2004 Modeling electricity prices with regime switching models. In: International Conference on Computational Science. Springer, Berlin, 859–867

  6. Hambly B, Howison S and Kluge T 2009 Modelling spikes and pricing swing options in electricity markets. Quantitative Finance. 9(8): 937–949

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Benth F E and Ortiz-Latorre S 2014 A pricing measure to explain the risk premium in power markets. SIAM Journal on Financial Mathematics. 5(1): 685–728

    Article  MathSciNet  MATH  Google Scholar 

  9. Pircalabu A and Benth F E 2017 A regime-switching copula approach to modeling day-ahead prices in coupled electricity markets. Energy Economics. 68: 283–302

    Article  Google Scholar 

  10. Mehrdoust F and and Noorani I 2021 Forward price and fitting of electricity Nord Pool market under regime-switching two-factor model. Mathematics and Financial Economics. 15(3): 501–543

    Article  MathSciNet  MATH  Google Scholar 

  11. Cartea A and Figueroa M G 2005 Pricing in electricity markets: a mean reverting jump diffusion model with seasonality. Applied Mathematical Finance. 12(4): 313–335

    Article  MATH  Google Scholar 

  12. David P S and Young V R 2005 Minimizing the probability of ruin when claims follow Brownian motion with drift. North American Actuarial Journal. 9(3): 110–128

    Article  MathSciNet  MATH  Google Scholar 

  13. Raphson J Analysis aequationum universalis. J Book R Soc Lond 1690

  14. Mehrdoust F, Najafi A R and Samimi H 2020 A mixed fractional Vasicek model and pricing Bermuda option on zero-coupon bonds. Sādhanā. 45(1): 1–12

    Article  MathSciNet  Google Scholar 

  15. Liang X and Young V R (2018) Minimizing the probability of ruin: Optimal per-loss reinsurance. Insurance Mathematics and Economics. 82: 181-190

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, 41938-1914, Rasht, Iran

    Alireza Najafi, Rahman Taleghani & Farshid Mehrdoust

Authors
  1. Alireza Najafi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rahman Taleghani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Farshid Mehrdoust
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alireza Najafi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Najafi, A., Taleghani, R. & Mehrdoust, F. Forward contract prices of electricity Nord Pool market: calibration and jump approximation. Sādhanā 48, 11 (2023). https://doi.org/10.1007/s12046-022-02056-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12046-022-02056-1

Keywords

Search

Navigation