雨量選擇權的定價與避險

Abstract

隨著全球氣候加速變遷，氣候所帶來的風險已逐漸受人們的重視；台灣由於地理位置關係，天然災害發生頻繁，尤其以颱風及梅雨所帶來的災害最為嚴重，而雨量是主要的因子，故本研究希望建立一個以雨量為基礎的衍生性商品，以提供企業及個人避險之用。本研究採用一般化的紐曼-史考特矩形跳動模型作為雨量模型，模型中假設鋒面的產生服從卜瓦松分配，每個鋒面可產生的雨雹數目及雨雹強度服從指數分配，每個雨雹的延時服從指數分配；另外，假設有兩種類型的雨雹。在參數估計方面，本研究採用改良式的霍普菲爾神經網路模型並配合無母數統計方法來確認所估計出的參數是適當的，並採用蒙地卡羅模擬法，來作雨量選擇權的定價。最後，以花蓮縣的瓜農避險為例，引進SCS曲線值模式，說明如何使用雨量選擇權作避險。

In recent years, the risk from weather changes has brought increasing attention all over the world. In Taiwan, typhoon and monsoon are the major sources of catastrophes, and the precipitation is the most important factor. This study tries to design a precipitation option for individuals and enterprises to hedge the rainfall risk. A generalized Neyman-Scott rectangular pulses model is adopted, where storms arrive in a Poisson process. The distributions of the numbers of rain cells in each storm and the intensity of each rain cell are geometric distributions, and the duration of each rain cell is an exponential random variable. The model is generalized by allowing each generated cell to be of two types. In parameter estimation, we use modified Hopfield neural network to solve nonlinear equations, and then we adopt Kolmogorov-Smirnov method to test whether the parameters are accetable. In valuation, we use Monte Carlo simulation to simulate the path of the precipitation and price the option. Finally, we provide the case analysis for watermelon hedging, and introduce the SCS curve number model to show how to use the precipitation option we developed.