This dissertation includes three topics. We first introduce the statistical properties of option pricing and literature related to the following topics. The first topic focuses on GARCH processes with Lévy innovation and their empirical analysis on TAIEX index options. Comparing to other popular option pricing models, the results show that the GARCH-Lévy processes fit well in-sample data. However, according to out-of- sample performances from three loss functions, there is no best model across all moneynesses. Although the VG option pricing model performs well at the money, the NGARCH option pricing model for in-the-money or out-of-the-money contracts is better than others. The second topic studies two baskets options under a multivariate normal inverse Gaussian model. The value of a geometric basket option can be expressed as an analytic-form formula and then its hedge ratios can be obtained from the partial derivatives of its pricing formula. Similarly, the value of an arithmetic basket option can be expressed as an analytic-form formula and then its hedge ratios can be obtained from the partial derivatives of its pricing formula. These options can be further applied to price related products, for example, multifund unit-linked insurance contracts. The numerical result supports the internal consistency of our closed-form analytical expressions for two basket options on two assets. The third topic studies the valuation of catastrophe insurance products. We survey the data about catastrophe events. Catastrophe occurrences can be forecasted, yet appear to have some rules, for example, the energy released by an earthquake can delay the next occurrence. Moreover, the 2-7 year cycle or pattern referred to as ENSO is a frequent natural reminder about the complex influences of the global ocean, atmosphere, and continental heat budget cycling and seasonality. The regime-switching compound Poisson process can be adopted to describe the jump-diffusion process under different states and thus be incorporated into the catastrophe loss or claim dynamics under different natural environments. Most catastrophe insurance contracts have provisions on some triggers to make loss claims or debt-forgiveness. Thus, we derive the pricing formulas of trigger options and then pricing catastrophe insurance products using an option-based method. The empirical evidences show that the regime-switching Poisson process in the RJSD model fits better than the pure Poisson process in a jump diffusion model in describing the arrival rates of great natural disasters over 1950-2006. We can further extend it to enough states to fit CAT arrival better, and then price other catastrophe insurance products more exactly.

When society fails to effectively integrate natural and constructed environments, one of the cataclysmic byproducts of this disconnect is an increased risk of natural disasters. On top of the devastation that is the aftermath of such disasters, poor planning and engineering decisions have detrimental effects on communities as they attempt to recover and rebuild. While there is an inherent difficulty in the quantification of the cost of human life, interruption in business operations, and damage to the properties, it is critical to develop plans and mitigation strategies to promote fast recovery. Traditionally insurance and reinsurance products have been used as a mitigation strategy for financing post-disaster recovery. However, there are number of problems associated with these models such as lack of liquidity, defaults, long litigation process, etc. In light of these problems, new Alternative Risk Transfer (ART) methods are introduced. The pricing of these risk mitigating instruments, however, has been mostly associated with the hazard frequency and intensity; and little recognition is made of the riskiness of the structure to be indemnified. This study proposes valuation models for catastrophe-linked ART products and insurance contracts in which the risks and value can be linked to the characteristics of the insured portfolio of constructed assets. The results show that the supply side ? structural parameters are as important as the demand ? hazard frequency, and are in a highly nonlinear relationship with financial parameters such as risk premiums and spreads.

90年代由於世界各地巨災頻傳，導致再保險人的承保能量嚴重不足，甚至於威脅到再保險人的清償能力，由於保險市場的容量已無法足夠涵蓋巨災的損失，再保險人開始尋找其他的風險移轉工具，因而在1992年芝加哥交易所保險證券化商品問世---巨災保險期貨。 本篇文章主要在介紹保險證券化最典型的兩個商品：巨災債券及巨災選擇權。首先針對巨災債券及巨災選擇權的商品內容加以描述；然後我們採用1970~2000年全球前四十大巨災損失作為巨災損失指數，透過定價模型對巨災債券及巨災選擇權作評價；最後分別對巨災債券及巨災選擇權的價格作敏感度分析，了解相關變數對巨災債券及巨災選擇權的價格的影響性。 在敏感度分析中，可看出巨災債券及巨災選擇權之價格具下列特性： (1) 在巨災債券方面，巨災債券價格和損失基準點、利息收回比率、本金收回比率、報酬率標準差呈正向關係，和報酬率、巨災發生次數呈反向關係； (2) 在巨災選擇權方面，損失資料分為理論巨災損失指數及實際損失指數，選擇權型態採用亞式選擇權，故選擇權價格有平均價格式及平均履約價格式兩種。 <1>在理論巨災損失指數選擇權方面，平均價格式選擇權價格和履約價、報酬率呈反向關係，和巨災發生次數呈正向關係，和標準差無關；平均履約價格式選擇權價格和報酬率呈反向關係，和巨災發生次數呈正向關係，和履約價、標準差無關； <2>在實際巨災損失指數選擇權方面，平均價格式選擇權價格和履約價、報酬率呈反向關係，和標準差無關；平均履約價格式選擇權價格和履約價、報酬率及標準差都呈反向關係。 希望藉由此篇論文之撰寫，將保險證券化的概念帶進國內保險領域，並提供保險業者了解另一種風險管理的方法。 / In the 1990s, many catastrophes occurred around the world, leading to a lack in reinsurers’ underwriting capacity and even, in some cases, threatening their solvency. Because the insurance market as a whole was unable to provide sufficient coverage for the catastrophe losses, reinsurers started looking for other risk transfer and management tools. In 1992, the first insurance securitization product was traded on the Chicago Board of Trade---Catastrophe Insurance Futures. This article aims to introduce two typical products: Catastrophe Bond (Cat Bond) and Catastrophe Option (Cat Option). First, we describe merchandise contents of Cat Bond and Cat Option. We then adopt global catastrophe losses as the catastrophe losses index for the period 1970-2000 and price models to evaluate Cat Bond and Cat Option. Finally, we conduct a sensitive analysis of Cat Bond and Cat Option prices. This allows us to understand the variables related to influencing the prices of Cat Bond and Cat Option. From the sensitive analysis, we realize that Cat Bond and Cat Option prices have the following characteristics: (1) From the Cat Bond aspect, the Cat Bond price has positive relationships with the loss trigger level, the receivable coupon ratio, the receivable principal ratio and the deviation error of return rate. It has negative relationships with the return rate and the times of catastrophe occurrences. (2) From the Cat Option aspect, we can distinguish between loss data to the theoretical catastrophe loss index and the actual catastrophe loss index. We adopt Asian Option as the option type, so that there are two types of option prices: the average price type of option price and the average exercise price type of option price. <1> From the aspect of the theoretical catastrophe loss index option, the average price type of option price has negative relationships with the exercise price and the return rate. It has a positive relationship with the times of catastrophe occurrence and has no relationships with the deviation error of the return rate. The average exercise price type of option price has negative relationships with the return rate. It has positive relationships with the times of catastrophe occurrence and has no relationships with the exercise price and the deviation error of the return rate. <2> From the aspect of the actual catastrophe loss index option, the average price type of option price has negative relationships with the exercise price and the return rate. It has no relationship with the deviation error of the return rate. The average exercise price type of option price has negative relationships with the exercise price, the return rate and the deviation error of the return rate. We hope that by writing this thesis, we can bring insurance securitization knowledge to the domestic insurance industry and can offer insurers an understanding of another risk management tool.

保險業及再保險業以往對於巨災危險的風險管理方式大部份都佼給全世界的再保險承保能量去承擔。然而從1995年開始，美國芝加哥交易所(CBOT)與產物損失部門(PCS)共同推出巨災保險選擇權，提供保險人以及再保險人利用國際金融市場移轉核保業務上所承擔之巨災危險的管道。此種業務上的巨災危險提供保險業處理巨災損失的新管道，例如產險業因為天然災害或是人為疏失所導致的鉅額核保損失以及壽險業的團體保險和健康保險的鉅額損失。巨災保險選擇權是一種新的衍生性金融商品，其交易標的物是專門針對保險業所承保的業務（尤其是巨災），因此如果運用得當，除了能有效的分散核保風險之外，更可以避免傳統的再保險契約所衍生的問題。 本研究在第一章首先說明台灣地區是地震、颱風以及水患等天然災害頗為集中的地區，因為傳統再保險的分散風險方式有其成本較高以及資訊不對稱的問題，所以保業以及再保險業應該考慮其他類型的危險管理策略。第二章以巨災保險選擇權評價的相關基礎理論為主要的架構，並且探討美國PCS所開發的巨災保險選擇權，並說明如何利用此種金融工具移轉保險與再保險人因地理上的核保因素所產生的風險。 第三章以及第四章討論模擬方法與分析模擬所得的結果，我們並利用情境分析的方式，探討在單位時間內，平均跳躍次數對於每一個模型中假設，交易標的物為損失指數時的影響，以及依此損失指數所得對於巨災保險選擇權價格之變化幅度。第五章則是歸納本研究所得的結果並且提出後續研究的建議。 / The insurance and reinsurance industries traditionally transfer their insurance risk of catastrophe disasters through the international reinsurance market. Since the capacity of the international reinsurance market is not always available to cover the entire risks. In 1995, CBOT (Chicago Board of Trade) and PCS (Property Claims Service) have begun trading the PCS catastrophe options Through the catastrophe options, the insures and reinsures could hedging their operating risks in the international financial market. These risks consist of large amount of underwriting losses from the natural disasters, personal default in property insurance, inflation of claims amount and the large claims in group insurance and health insurance. The loss ratios of the insured business are trading through the catastrophe options. Hedging the operating risks of the insures and reinsures in the financial market could effectively reduce the costs and avoid the complexity from the reinsurance contracts. In this study, we have reviewed the development of the catastrophe option. Asian style call options are illustrated to monitor the process of option pricing. The trading loss ratios are modeled through lognormal distribution based on the claim experience collected from 1970-1996. The methodology of pricing the modified options based on pure jump model proposed by Cox, et al (1976) and the jump diffusion model proposed by Merton (1976) are discussed. Computer simulations and scenario analysis are performed to investigate the pricing of Asian style catastrophe option under various proposed models. Sensitivity analysis is also completed at various parameters in the jump process. Finally, comments on future works and the limitation of the proposed risk-transfer mechanism using catastrophe options are discussed.