台灣巨災超額再保險契約與評價

過去數年，雖然巨災風險證券化在台灣已被廣泛討論，但在市場尚未成熟前及有限的傳統承保能量下，由民間配合政府的再保險仍為主要可行的移轉風險方式。本文首先論述適合台灣的政府巨災超額再保契約之原理與架構，再根據台灣地區天然巨災實際損害統計資料，使用極值理論中的門檻（POT）模型來配適其損失之尾端分配，並針對巨災損失的特性，以在純粹跳躍過程下的財務選擇權原理來計算政府巨災再保險契約的價值，以作為評價的理論基礎。結果顯示台灣天然巨災尾部分配相當適合以形狀參數不為零的一般化柏拉圖（GPD）分配來描述。但若以對數常態分配建構尾部分配，則政府再保契約價值可能低估，反之，若以指數分配建構尾部分配則可能高估。隨著契約不同上下限差距的變化，再保契約價值也將隨之呈非線性改變。我們也發現當門檻值增加，契約價值也隨之上升。本文的評價方法與結果可作為未來政府設計更完備巨災超額再保契約及底價訂定的參考。

關鍵字

巨災；超額再保險；跳躍過程

並列摘要

Although the securitization of catastrophe risk in Taiwan had been widely advocated by scholars and regulator recently, traditional reinsurance still plays as a major risk transfer tool for the property and liability insurer because of the immaturity of catastrophe derivative market. In this paper, we first address the rationales and, subsequently, price the ongoing government excess of loss reinsurance contract in Taiwan. We fit the loss distributions by using most updated catastrophe data. More specifically, the Generalized Pareto distribution (GPD) from extreme value theory is undertaken to describe the tail distribution of Taiwan's natural disaster. Our results indicate that GPD is a decent choice for loss data fitting compared to other distributions. Finally, the contract's values are computed by mean of a pure-jump based financial option model. According to the simulation results, we find that the contract value may be underestimated if the excess of loss distribution is fitted by lognormal. Conversely, exponential distribution may overestimate the true contract value. In addition, given the computed contract values under various triggers/caps, we find that it may vary in accordance with different thresholds. Our results may serve as a supportive function on the design and pricing of government catastrophe XOL reinsurance contract in Taiwan.