- 學位論文
基於溫度與雨量之氣候選擇權評價模型
A Pricing Model of Weather Derivatives Based on Temperature and Precipitation
摘要
由於降雨量與最低溫度是影響台灣農業極大的天氣因素，農民常因暴雨與低溫帶來極大的損失，為了規避此一損失，以氣候因素為標的的衍生性金融商品也因應而生。然大部分的氣候選擇權均侷限於單一因素 (溫度或雨量) 之探討；本研究則探討同時考量降雨量與最低溫度之選擇權。因為溫度及雨量資料均具有具有季節性且雨量之變異極大，所以將資料取對數後再進行年差分以得到定態性。 本研究先將對數差分後的溫度及雨量數列分別配適殘差為t分配之單變量ARMA-GARCH模型，再以兩數列之標準化殘差建立邊際分配，利用copula函數建立聯合機率分配函數。接著利用最大概似估計法估計copula函數的參數。本研究考慮五種常見的copula：Gaussian copula、t copula、Gumbel copula、Frank copula、Clayton copula，其中Frank copula為最適合的copula連結函數。 本研究的評價變數採用溫度與雨量等權重之線性組合，再以評價日之前後各20天為窗口 (window)，估計Frank copula動態相關係數Spearman’s 。經由此動態相關係數及單變量ARMA-GARCH模型所得到溫度與雨量之動態條件變異數，可計算評價變數之動態條件變異數，代入歐式選擇權的買權與賣權評價公式即可求出一個隨時間t變動而改變的動態評價模型。 關鍵字：copula函數；Garch模型；動態相關係數；Spearman’s rho ；評價模型
並列摘要
The major weather factors which affect the agriculture of Taiwan are daily lowest temperature and amount of precipitation. Farmers always lost their harvest due to lower temperature or heavy rainfall. To prevent the agriculture loss caused by extreme weather, some derivatives of weather are established. Most of the weather options are limited in single factor. This study considers both daily lowest temperature and amount of precipitation to build a bivariate pricing model of weather option. Since seasonality is found in daily lowest temperature and amount of precipitation and variance of precipitation is large, the logarithm transformation and annually difference are applied to obtain stationary of the time series. This study builds univariate ARMA-GARCH model with t innovation for each difference of logarithm series first. Then, standardized residuals are adopted as marginal distributions. And the joint distribution is built by Copula function. The parameter of Copula function is estimated by the maximum likelihood method. Five common copula: Gaussian copula, t copula, Gumbel copula, Frank copula, and Clayton copula are considered. In which, the Frank copula is the most appropriate as the link function. The pricing variable of this study is an equal weighted linear combination of daily lowest temperature and amount of precipitation. A window of 20 days before the pricing day is applied to estimate the dynamic correlation coefficient, Spearman’s , by Frank copula. Through the dynamic correlation coefficient and the conditional variances obtained by univariate ARMA-GARCH model, the volatility of pricing variable can be calculated. Finally, the call option and put option can be obtained by the European options formula. Keywords: copula function; GARCH model; dynamic correlation coefficient; Spearman’s rho; pricing model