State Price Densities implied from weather derivatives

Wolfgang Härdle, Brenda López-Cabrera and Huei-wen Teng
Authors registered in the RePEc Author Service: Brenda López-Cabrera

No 2013-026, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

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.

Keywords: weather derivatives; temperature derivatives; HDD; CDD; SPD; mixture; quadrature; Bayesian; Option trading Strategies; illiquid (search for similar items in EconPapers)
JEL-codes: C11 C22 C58 G12 G13 G19 G22 N23 N53 (search for similar items in EconPapers)
Date: 2013
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Journal Article: State price densities implied from weather derivatives (2015)
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