TY - JOUR

T1 - State price densities implied from weather derivatives

AU - Karl Härdle, Wolfgang

AU - López-Cabrera, Brenda

AU - Teng, Huei-Wen

PY - 2015/9/1

Y1 - 2015/9/1

N2 - A State Price Density (SPD) is the density function of a risk neutral equivalent martingale measure for option pricing, and is indispensable 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 semiparametric methods were preferred because they can avoid model mis-specification of the underlying. However, these methods usually require a large data set to achieve desired convergence properties. 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 data sparsity issue. As illustration, we calibrate the SPD for weather derivatives, a classical example of incomplete markets with financial contracts payoffs linked to non-tradable assets, namely, weather indices. Finally, we study related weather derivatives data and the dynamics of the implied SPDs.

AB - A State Price Density (SPD) is the density function of a risk neutral equivalent martingale measure for option pricing, and is indispensable 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 semiparametric methods were preferred because they can avoid model mis-specification of the underlying. However, these methods usually require a large data set to achieve desired convergence properties. 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 data sparsity issue. As illustration, we calibrate the SPD for weather derivatives, a classical example of incomplete markets with financial contracts payoffs linked to non-tradable assets, namely, weather indices. Finally, we study related weather derivatives data and the dynamics of the implied SPDs.

KW - Bayesian

KW - CDD

KW - Data sparsity

KW - HDD

KW - Quadrature

KW - State Price Density

KW - Temperature derivatives

KW - Weather derivatives

UR - http://www.scopus.com/inward/record.url?scp=84930938402&partnerID=8YFLogxK

U2 - 10.1016/j.insmatheco.2015.05.001

DO - 10.1016/j.insmatheco.2015.05.001

M3 - Article

AN - SCOPUS:84930938402

VL - 64

SP - 106

EP - 125

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

ER -