Valuation of Precipitation Contracts

This thesis is to develop a method to value the initial price of precipitation contracts based on the daily precipitation data from Toronto Pearson region. Daily precipitation data is analyzed by fitting an appropriate statistical distribution. Then perform a monthly precipitation time series model, to detect the trend and seasonality. A continuous-time model is given that is driven by a L´evy process. The most important technique in this thesis is the risk-neutral pricing formula that is proposed to compute the initial price under the equivalent martingale process by Esscher transform. The numerical results are finished by inverse Fourier transform and trapezoid method. The pricing results are compared with Monte Carlo simulation. A sensitivity analysis is given based on a variety of parameters from the pricing method. At the end, there is a conclusion and future work.