台灣地區巨災之時間序列相關研究--以歷年颱風損失為例

Abstract

在巨災債券的評價上，過去文獻大都假設巨災的發生損失頻率服從卜瓦松分配，損失幅度服從對數常態分配，也就是說，巨災的損失幅度在時間序列上為獨立相關，應由ARMA(0,0)模型所產生，然而，此假設卻可能導致巨災債券價格被低估或高估。 因此，本篇論文的研究目的為檢定巨災損失幅度在時間序列上為獨立相關的假設，以台灣地區歷年颱風損失金額為研究對象，為其配置ARIMA模型。颱風損失資料的來源為農業統計年報及內政部消防署公佈的台灣地區天然災害損失統計。 實證結果發現台灣的每年颱風損失此一時間序列資料非由ARMA(0,0)模型所產生，且模型參數估計結果指出過去幾期的白噪音對於當期颱風損失金額會有正向的影響。此外，消除通膨因子並不會改變台灣地區颱風總損失金額與農作物颱風損失金額這兩個時間序列資料的模型。因此，建議未來台灣若發行與颱風風險相連結的巨災商品時，可考慮將時間序列模型納入評價模型中，有助降低價格被錯估的機率。

Previous research applied the assumption that catastrophe loss followed a pure Poisson process, and the loss severity followed an independently identical lognormal distribution when pricing the catastrophe bonds. In other words, catastrophe loss is time series independent and is generated from an ARMA(0,0) model. However, the assumption may result in under-pricing or over-pricing the catastrophe bonds. To test the assumption that catastrophe loss is time series independent, I will fit the ARIMA model for the typhoon loss occurring in Taiwan. The loss data is collected from the agricultural statistics released by Council of Agriculture and the disaster loss statistics released by National Fire Agency, Ministry Of The Interior. The result indicates that the time series data of annual typhoon loss in Taiwan is not generated from an ARMA(0,0) model and the past white noises have positive effect on current typhoon loss. Besides, whether to eliminate the inflation factor does not change the time series model of total typhoon loss and agricultural typhoon loss occurring in Taiwan. For future research, it is suggested that the possibility of mispricing the catastrophe bonds might be reduced if the time series model is combined into the pricing model.