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State Price Densities implied from weather derivatives

Author

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  • Wolfgang Karl Härdle
  • Brenda López-Cabrera
  • Huei-Wen Teng

Abstract

A State Price Density (SPD) is the density function of a risk neutral equivalent martingale measure for option pricing, and is indispensible for exotic option pricing and portfolio risk management. Many approaches have been proposed in the last two decades to calibrate a SPD using financial options from the bond and equity markets. Among these, non and semi parametric methods were preferred because they can avoid model mis-specification of the underlying and thus give insight into complex portfolio propelling. However, these methods usually require a large data set to achieve desired convergence properties. Despite recent innovations in finan- cial and insurance markets, many markets remain incomplete and there exists an illiquidity issue. One faces the problem in estimation by e.g. kernel techniques that there are not enough observations locally available. For this situation, we employ a Bayesian quadrature method because it allows us to incorporate prior assumptions on the model parameters and hence avoids problems with data sparsity. It is able to compute the SPD of both call and put options simultaneously, and is particularly robust when the market faces the illiquidity issue. By comparing our approach with other approaches, we show that the traditional way of estimating the SPD by differ- entiating an interpolation of option prices does not hold in practice. As illustration, we calibrate the SPD for weather derivatives, a classical example of incomplete mar- kets with financial contracts payoffs linked to non-tradable assets, namely, weather indices. Finally, we study the dynamics of the implied SPD's and related to weather data.

Suggested Citation

  • Wolfgang Karl Härdle & Brenda López-Cabrera & Huei-Wen Teng, 2013. "State Price Densities implied from weather derivatives," SFB 649 Discussion Papers SFB649DP2013-026, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2013-026
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Brenda López Cabrera & Martin Odening & Matthias Ritter, 2013. "Pricing Rainfall Derivatives at the CME," SFB 649 Discussion Papers SFB649DP2013-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. 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.
    3. Taboga, Marco, 2016. "Option-implied probability distributions: How reliable? How jagged?," International Review of Economics & Finance, Elsevier, vol. 45(C), pages 453-469.

    More about this item

    Keywords

    Weather derivatives; temperature derivatives; HDD; CDD; SPD; mixture; quadrature; Bayesian; Option trading Strategies; illiquid;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G19 - Financial Economics - - General Financial Markets - - - Other
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • N23 - Economic History - - Financial Markets and Institutions - - - Europe: Pre-1913
    • N53 - Economic History - - Agriculture, Natural Resources, Environment and Extractive Industries - - - Europe: Pre-1913

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