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研究生： 桂正翰
Kuei, Cheng-Han
論文名稱： 以遞迴估算法評價巨災衍生性商品
A Recursive Evaluation Approach to Price Catastrophe Derivatives
指導教授： 劉裕宏
Liu, Yu-hong
學位類別： 碩士
Master
系所名稱： 管理學院 - 財務金融研究所
Graduate Institute of Finance
論文出版年： 2006
畢業學年度： 94
語文別： 英文
論文頁數： 43
中文關鍵詞： 巨災衍生性商品 、遞迴估算法 、複合波桑隨機過程與機率分配
外文關鍵詞： Recursive Evaluation Approach, Compound Poisson Process and Distribution, Catastrophe Insurance Derivative
相關次數： 點閱：176  下載：12 
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    • 　　透過假設總合巨災損失指數隨機過程服從複合波桑隨機過程,並採用遞迴估算法來運算複合波桑機率分配,可以建構出一個更為實用的巨災衍生性商品評價模式。

    　　以本文中發展出來的評價模式來評價ISO巨災期貨與PCS巨災選擇權,不僅可以大幅簡化計算機率分配的過程,而且能夠搭配保險業界的機率精算技術以找出更為精確的估計價格。

    　　Assuming the underlying aggregate catastrophe claims process as the compound Poisson process and applying recursive evaluation approach to compute the compound Poisson distribution,we can construct a more practical pricing model of catastrophe insurance derivatives,such as the ISO catastrophe futures and the PCS catastrophe options. The pricing model derived in this thesis simplifies the procedure of probability computation especially in the huge catastrophe claim occurrence, and also helps the hedging insurance companies easily apply their probability assessing techniques to find the prices of these derivatives.

    摘要 i Abstract ii 誌謝 iii 1 Introduction 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Motivation and Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Literature Review 4 2.1 Catastrophe Insurance Derivatives . . . . . . . . . . . . . . . . . . . . . . 4 2.1.1 The ISO Index and Derivatives . . . . . . . . . . . . . . . . . . . . 4 2.1.2 The PCS Index and Derivatives . . . . . . . . . . . . . . . . . . . 5 2.2 An Asian Option Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Cummins and Geman (1993) . . . . . . . . . . . . . . . . . . . . . 7 2.2.2 Cummins and Geman (1995) . . . . . . . . . . . . . . . . . . . . . 8 2.3 A Randomized Operational Time Approach . . . . . . . . . . . . . . . . . 10 2.4 A Stochastic Time Change Approach . . . . . . . . . . . . . . . . . . . . . 11 2.5 An Actuarial Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.6 An Inverse Fourier Transform Approach . . . . . . . . . . . . . . . . . . . 14 2.7 Other Relevant Literatures . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 Methodology 17 3.1 The Generalized Aggregate Claims Process . . . . . . . . . . . . . . . . . 17 3.1.1 Introducing Compound Poisson Process and Distribution . . . . . . 17 3.1.2 Properties of Compound Poisson Distribution . . . . . . . . . . . . 19 3.2 Recursive Evaluation of Compound Poisson Distribution . . . . . . . . . . 20 3.3 Application of Pricing Catastrophe Derivatives . . . . . . . . . . . . . . . 21 3.3.1 The Adjusted Aggregate Claims Process . . . . . . . . . . . . . . . 22 3.3.2 The ISO Catastrophe Futures . . . . . . . . . . . . . . . . . . . . . 24 3.3.3 The PCS Catastrophe Options . . . . . . . . . . . . . . . . . . . . 26 4 Numerical Results 28 4.1 Base Value and Simplicity Assumption . . . . . . . . . . . . . . . . . . . . 28 4.2 The Result of the PCS Call and Put Prices . . . . . . . . . . . . . . . . . . 29 4.3 The Effect of Different Claim Occurrence Frequencies . . . . . . . . . . . 31 4.4 The Impact of Various Claim Amount Distributions . . . . . . . . . . . . . 33 4.5 Comparing with Monte Carlo Simulation . . . . . . . . . . . . . . . . . . 36 4.6 A Hedging Example of the PCS Options . . . . . . . . . . . . . . . . . . . 37 5 Conclusion 39 Bibliography 41

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