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Statistical analysis of model risk concerning temperature residuals and its impact on pricing weather derivatives

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  • Ahčan, Aleš

Abstract

In this paper we model the daily average temperature via an extended version of the standard Ornstein Uhlenbeck process driven by a Levy noise with seasonally adjusted asymmetric ARCH process for volatility. More precisely, we model the disturbances with the Normal inverse Gaussian (NIG) and Variance gamma (VG) distribution. Besides modelling the residuals we also compare the prices of January 2010 out of the money call and put options for two of the Slovenian largest cities Ljubljana and Maribor under normally distributed disturbances and NIG and VG distributed disturbances. The results of our numerical analysis demonstrate that the normal model fails to capture adequately tail risk, and consequently significantly misprices out of the money options. On the other hand prices obtained using NIG and VG distributed disturbances fit well to the results obtained by bootstrapping the residuals. Thus one should take extreme care in choosing the appropriate statistical model.

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  • Ahčan, Aleš, 2012. "Statistical analysis of model risk concerning temperature residuals and its impact on pricing weather derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 131-138.
    • Handle: RePEc:eee:insuma:v:50:y:2012:i:1:p:131-138
    DOI: 10.1016/j.insmatheco.2011.10.005
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    References listed on IDEAS

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    1. Sean D. Campbell & Francis X. Diebold, 2005. "Weather Forecasting for Weather Derivatives," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 6-16, March.
    2. Wolfgang Karl Härdle & Brenda López Cabrera, 2012. "The Implied Market Price of Weather Risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(1), pages 59-95, February.
    3. Peter Alaton & Boualem Djehiche & David Stillberger, 2002. "On modelling and pricing weather derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(1), pages 1-20.
    4. M. Davis, 2001. "Pricing weather derivatives by marginal value," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 305-308, March.
    5. Fred Espen Benth & Jurate Saltyte-Benth, 2005. "Stochastic Modelling of Temperature Variations with a View Towards Weather Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(1), pages 53-85.
    6. Jewson,Stephen & Brix,Anders, 2005. "Weather Derivative Valuation," Cambridge Books, Cambridge University Press, number 9780521843713, September.
    7. Dorje Brody & Joanna Syroka & Mihail Zervos, 2002. "Dynamical pricing of weather derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 2(3), pages 189-198.
    8. Hélène Hamisultane, 2007. "Extracting Information from the Market to Price the Weather Derivatives," Working Papers halshs-00079192, HAL.
    9. Taylor, James W. & Buizza, Roberto, 2006. "Density forecasting for weather derivative pricing," International Journal of Forecasting, Elsevier, vol. 22(1), pages 29-42.
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    Cited by:

    1. López Cabrera, Brenda & Odening, Martin & Ritter, Matthias, 2013. "Pricing rainfall futures at the CME," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4286-4298.

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    More about this item

    Keywords

    Weather derivatives; Levy models; Asymmetric ARCH; Esscher transform; Model risk;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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