Laplace Transform Method and Its Applications for Weather Derivatives

Abstract

In this thesis we deal with the most efficient methods for numerical Laplace inversion and analyze the effect of roundoff errors. There are three issues in the control of numerical Laplace inversion: the choice of contour, its parameterization and numerical quadrature. We extend roundoff error control to the case of numerical inversion for hyperbolic contour. Also in order to examine the effect of roundoff error, computation is carried out both in double-precision and multi-precision, the latter which provides better understanding of the numerical Laplace inversion algorithms. We analyze temperature data for Seoul based on a well defined daily average temperature and consider related weather derivatives. The temperature data exhibit some quite distinctive features, compared to other cities that have been considered before. Due to these characteristics, seasonal variance and oscillation in Seoul is more apparent in winter and less evident in summer than in the other cities. We construct a deterministic model for the average temperature and then simulate future weather patterns, before pricing various weather derivative options and calculating the market price of risk. And Laplace transform method is applicable for solving the partial differential equation of weather derivatives.