Skip to main content

Advertisement

SpringerLink
Log in

Wind Derivatives: Modeling and Pricing

  • Published:
Computational Economics Aims and scope Submit manuscript

Abstract

Wind is considered to be a free, renewable and environmentally friendly source of energy. However, wind farms are exposed to excessive weather risk since the power production depends on the wind speed, the wind direction and the wind duration. This risk can be successfully hedged using a financial instrument called weather derivatives. In this study the dynamics of the wind generating process are modeled using a non-parametric non-linear wavelet network. Our model is validated in New York. The proposed methodology is compared against alternative methods, proposed in prior studies. Our results indicate that wavelet networks can model the wind process very well and consequently they constitute an accurate and efficient tool for wind derivatives pricing. Finally, we provide the pricing equations for wind futures written on two indices, the cumulative average wind speed index and the Nordix wind speed index.

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

Similar content being viewed by others

References

  • Ailliot P., Monbet V., Prevosto M. (2006) An autoregressive model with time-varying coefficients for wind fields. Envirometrics 17: 107–117

    Article  Google Scholar 

  • Alaton P., Djehince B., Stillberg D. (2002) On modelling and pricing weather derivatives. Applied Mathematical Finance 9: 1–20

    Article  Google Scholar 

  • Alexandridis A. (2010) Modelling and pricing temperature derivatives using wavelet networks and wavelet analysis. University of Macedonia, Thessaloniki, Greece

    Google Scholar 

  • Alexiadis M. C., Dokopoulos P. S., Sahsamanoglou H. S., Manousaridis I. M. (1998) Short-term forecasting of wind speed and related electrical power. Solar Energy 63(1): 61–68

    Article  Google Scholar 

  • Barbounis T. G., Theocharis J. B., Alexiadis M. C., Dokopoulos P. S. (2006) Long-term wind speed and power forecasting using local recurrent neural network models. IEEE Transactions on Energy Conversion 21(1): 273–284

    Article  Google Scholar 

  • Bellini, F. (2005). The weather derivatives market: Modelling and pricing temperature. Ph.D Thesis, University of Lugano, Lugano, Switzerland.

  • Benth F. E. (2004) Option theory with stochastic analysis. Springer, Berlin

    Book  Google Scholar 

  • Benth, F.E., Hardle, W. K., & Lopez Cabrera, B. (2009). Pricing of Asian temperature risk. SFB649 Working Paper. Berlin: Humboldt-Universitat zu Berlin.

  • Benth F. E., Saltyte-Benth J. (2007) The volatility of temperature and pricing of weather derivatives. Quantitative Finance 7(5): 553–561

    Article  Google Scholar 

  • Benth F. E., Saltyte-Benth J. (2009) Dynamic pricing of wind futures. Energy Economics 31: 16–24

    Article  Google Scholar 

  • Benth J. r. a., Benth F. E. (2010) Analysis and modelling of wind speed in New York. Journal of Applied Statistics 37(6): 893–909

    Article  Google Scholar 

  • Beyer, H. G., Degner, T., Hausmann, J., Hoffmann, M., & Rujan, P. (1994). Short-term prediction of wind speed and power outputof a wind turbine with neural netwroks. In 2nd European Congress on Intelligent Techniques and Soft Computing, Aachen, Germany, pp. 20–23.

  • Billinton R., Chen H., Ghajar R. (1996) Time-series models for reliability evaluation of power systems including wind energy. Microelectronics and Reliability 36(9): 1253–1261

    Article  Google Scholar 

  • Brett A. C., Tuller S. E. (1991) The autocorrelation of hourly wind speed observations. Journal of Applied Meteorology 30(6): 823–833. doi:10.1175/1520-0450(1991)030<0823:TAOHWS>2.0.CO;2

    Article  Google Scholar 

  • Brockwell P. J., Marquardt T. (2005) Levy-driven and fractionality integrated ARMA process with continuous time parameter. Statistica Sinica 15: 477–494

    Google Scholar 

  • Brody C. D., Syroka J., Zervos M. (2002) Dynamical pricing of weather derivatives. Quantitave Finance 2: 189–198

    Article  Google Scholar 

  • Brown B. G., Katz R. W., Murphy A. H. (1984) Time-series models to simulate and forecast wind speed and wind power. Journal of Climate and Applied Meteorology 23: 1184–1195

    Article  Google Scholar 

  • Cao, M., & Wei, J. (2003). Weather derivatives: A new class of financial instruments. Working Paper, University of Toronto, Toronto.

  • Cao M., Wei J. (2004) Weather Derivatives valuation and market price of weather risk. Journal of Future Markets 24(1): 1065–1089

    Article  Google Scholar 

  • Caporin, M., & Pres, J. (2010). Modelling and forecasting wind speed intensity for weather risk management. Computational Statistics & Data Analysis. doi:10.1016/j.csda.2010.06.019.

  • Castino F., Festa R., Ratto C. F. (1998) Stochastic modelling of wind velocities time-series. Journal of Wind Engineering and Industrial Aerodynamics 74(76): 141–151

    Article  Google Scholar 

  • Celik A. N. (2004) A statistical analysis of wind power density based on the Weibull and Rayleigh models at the southern region of Turkey. Renewable Energy 29(4): 593–604. doi:10.1016/j.renene.2003.07.002

    Article  Google Scholar 

  • Challis, S. (1999). Bright forecast for profits. Reactions, June edition.

  • CME.(2005). An Introduction to CME Weather Products. http://www.cme.com/edu/res/bro/cmeweather. Accessed January 2007.

  • Cripps E., Nott D., Dunsmuir W. T. M., Wikle C. (2005) Space-time modelling of sydney harbour winds. Australian & New Zealand Journal of Statistics 47(1): 3–17. doi:10.1111/j.1467-842X.2005.00368.x

    Article  Google Scholar 

  • Daniel A. R., Chen A. A. (1991) Stochastic simulation and forecasting of hourly average wind speed sequences in Jamaica. Solar Energy 46(1): 1–11

    Article  Google Scholar 

  • Dorfleitner, G., & Wimmer, M. (2010). The pricing of temperature futures at the chicago mercantile exchange. Journal of Banking & Finance. doi:10.1016/j.bankfin.2009.12.004.

  • Dorvlo A. S. S. (2002) Estimating wind speed distribution. Energy Conversion and Management 43(17): 2311–2318. doi:10.1016/s0196-8904(01)00182-0

    Article  Google Scholar 

  • Garcia A., Torres J. L., Prieto E., de Francisco A. (1998) Fitting wind speed distributions: A case study. Solar Energy 62(2): 139–144. doi:10.1016/s0038-092x(97)00116-3

    Article  Google Scholar 

  • Hanley M. (1999) Hedging the force of nature. Risk Professional 1: 21–25

    Google Scholar 

  • Härdle W. K., Cabrera B. L. (2011) The implied market price of weather risk. Applied Mathematical Finance 19(1): 59–95

    Article  Google Scholar 

  • Haslett J., Raftery A. E. (1989) Space-time modelling with long-memory dependence: Assessing Ireland’s wind power resource. Journal of the Royal Statistical Society. Series C (Applied Statistics) 38(1): 1–50

    Google Scholar 

  • Huang H.-H., Shiu Y.-M., Lin P.-S. (2008) HDD and CDD option pricing with market price of weather risk for Taiwan. The Journal of Futures Markets 28(8): 790–814

    Article  Google Scholar 

  • Huang Z., Chalabi Z. S. (1995) Use of time-series analysis to model and forecast wind speed. Journal of Wind Engineering and Industrial Aerodynamics 56: 311–322

    Article  Google Scholar 

  • Jaramillo O. A., Borja M. A. (2004) Wind speed analysis in La Ventosa, Mexico: A bimodal probability distribution case. Renewable Energy 29(10): 1613–1630. doi:10.1016/j.renene.2004.02.001

    Article  Google Scholar 

  • Jewson, S., Brix, A., & Ziehmann, C. (2005). Weather derivative valuation: The meteorological, statistical, financial and mathematical foundations. Cambridge, UK: Cambridge University Press.

  • Justus C.G., Hargraves W.R., Mikhail A., Graber D. (1978) Methods for estimating wind speed frequency distributions. Journal of Applied Meteorology (United States) 17(3): 350–385

    Article  Google Scholar 

  • Kamal L., Jafri Y. Z. (1997) Time-series models to simulate and forecast hourly averaged wind speed in Quetta, Pakistan. Solar Energy 61(1): 23–32

    Article  Google Scholar 

  • Kavak Akpinar E., Akpinar S. (2005) A statistical analysis of wind speed data used in installation of wind energy conversion systems. Energy Conversion and Management 46(4): 515–532. doi:10.1016/j.enconman.2004.05.002

    Article  Google Scholar 

  • Kavasseri R. G., Seetharaman K. (2009) Day-ahead wind speed forecasting using f-ARIMA models. Renewable Energy 34(5): 1388–1393. doi:10.1016/j.renene.2008.09.006

    Article  Google Scholar 

  • Lei M., Shiyan L., Chuanwen J., Hongling L., Yan Z. (2009) A review on the forecasting of wind speed and generated power. Renewable and Sustainable Energy Reviews 13(4): 915–920. doi:10.1016/j.rser.2008.02.002

    Article  Google Scholar 

  • Lucas R. (1978) Asset prices in an exchange economy. Econometrica 46: 1429–1445

    Article  Google Scholar 

  • Martin M., Cremades L. V., Santabarbara J. M. (1999) Analysis and modelling of time-series of surface wind speed and direction. International Journal of Climatology 19: 197–209

    Article  Google Scholar 

  • Mohandes M. A., Halawani T. O., Rehman S., Hussain A. A. (2004) Support vector machines for wind speed prediction. Renewable Energy 29(6): 939–947. doi:10.1016/j.renene.2003.11.009

    Article  Google Scholar 

  • Mohandes M. A., Rehman S., Halawani T. O. (1998) A neural networks approach for wind speed prediction. Renewable Energy 13(3): 345–354. doi:10.1016/s0960-1481(98)00001-9

    Article  Google Scholar 

  • Moody, J. E., & Utans, J. (1992). Principled architecture selection for neural networks: Applications to corporate bond rating prediction. In A. P. Refenes (Ed.), Neural networks in the capital markets. New York: Wiley.

  • More A., Deo M. C. (2003) Forecasting wind with neural networks. Marine Structures 16: 35–49

    Article  Google Scholar 

  • Nfaoui H., Buret J., Sayigh A. A. M. (1996) Stochastic simulation of hourly average wind speed sequences in Tangiers (Morocco). Solar Energy 56(3): 301–314. doi:10.1016/0038-092x(95)00103-x

    Article  Google Scholar 

  • Nielsen, T. S., Madsen, H., Nielsen, H. A., Pinson, P., Kariniotakis, G., Siebert, N., et al. (2006). Short-term wind power forecasting using advanced statistical methods. Paper presented at the European wind energy conference, EWEC, Athens, Greece.

  • Pinson, P., & Kariniotakis, G. N. (2003). Wind power forecasting using fuzzy neural networks enhanced with on-line prediction risk assessment. In Power Tech Conference Proceedings, IEEE Bologna, 23–26 June 2003 (Vol. 2, pp. 8 pp. Vol.2)

  • Rehman S., Halawani T. O. (1994) Statistical characteristics of wind in Saudi Arabia. Renewable Energy 4(8): 949–956. doi:10.1016/0960-1481(94)90229-1

    Article  Google Scholar 

  • Richards T. J., Manfredo M. R., Sanders D. R. (2004) Pricing weather derivatives. American Journal of Agricultural Economics 4(86): 1005–1017

    Article  Google Scholar 

  • Sfetsos A. (2000) A comaprison of various forecasting techniques applied to mean hourly wind speed time-series. Renewable Energy 21: 23–35

    Article  Google Scholar 

  • Sfetsos A. (2002) A novel approach for the forecasting of mean hourly wind speed time series. Renewable Energy 27: 163–174

    Article  Google Scholar 

  • Tol R. S. J. (1997) Autoregressive conditional heteroscedasticity in daily wind speed measurements. Theoretical and Applied Climatology 56: 113–122

    Article  Google Scholar 

  • Tolman H. L., Booij N. (1998) Modeling wind waves using wavenumber-direction spectra and a variable wavenumber grid. The Global Atmosphere and Ocean System 6: 295–309

    Google Scholar 

  • Torres J. L., Garcia A., De Blas M., De Francisco A. (2005) Forecast of hourly average wind speed with ARMA models in Navarre (Spain). Solar Energy 79: 65–77

    Article  Google Scholar 

  • Tuller S. E., Brett A. C. (1984) The characteristics of wind velocity that favor the fitting of a weibull distribution in wind speed analysis. Journal of Climate and Applied Meteorology 23(1): 124–134

    Article  Google Scholar 

  • Turvey C.G. (2005) The pricing of degree-day weather options. Agricultural Finance Review Spring 2005: 59–85

    Article  Google Scholar 

  • Wilks, D. S. (2011). Statistical methods in the atmospheric sciences, Vol. 100. International Geophysics Series, 3rd edn. Academic Press, Oxford, UK.

  • WRMA. (2010). Weather derivatives volume plummets. www.wrma.org/pdf/weatherderivativesvolumeplummets.pdf. Accessed January 2010.

  • Xu W., Odening M., Musshof O. (2008) Indifference pricing of weather derivatives. American Journal of Agricultural Economics 90(4): 979–993

    Article  Google Scholar 

  • Yamada, Y. (2008). Simultaneous optimization for wind derivatives based on prediction errors. In Americal Control Conference, Washington, USA, June 11–13 (pp. 350–355).

  • Zapranis A., Alexandridis A. (2008) Modelling temperature time dependent speed of mean reversion in the context of weather derivetive pricing. Applied Mathematical Finance 15(4): 355–386

    Article  Google Scholar 

  • Zapranis A., Alexandridis A. (2009) Weather derivatives pricing: Modelling the seasonal residuals variance of an ornstein-uhlenbeck temperature process with neural networks. Neurocomputing 73: 37–48

    Article  Google Scholar 

  • Zapranis, A., & Alexandridis, A. (2010). Modeling and forecasting cumulative average temperature and heating degree day indices for weather derivative pricing. Neural Computing & Applications, 1–15. doi:10.1007/s00521-010-0494-1.

  • Zapranis A., Refenes A. P. (1999) Principles of neural model indentification, selection and adequacy: With applications to financial econometrics. Springer, Berlin

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF, UK

    A. Alexandridis

  2. Department of Accounting and Finance, University of Macedonia of Economics and Social Studies, 156 Egnatia St., 54006, Thessaloniki, Greece

    A. Zapranis

Authors
  1. A. Alexandridis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Zapranis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Alexandridis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alexandridis, A., Zapranis, A. Wind Derivatives: Modeling and Pricing. Comput Econ 41, 299–326 (2013). https://doi.org/10.1007/s10614-012-9350-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10614-012-9350-y

Keywords

Search

Navigation