【作者】 闵世立；

【导师】 邓国和；

【作者基本信息】 广西师范大学 ， 概率论与数理统计， 2012， 硕士

【摘要】 巨灾风险是指突发性、不可预料、无法回避而且危害性极大的自然灾难性事件所产生的风险.近几十年来,世界范围内自然灾害(地震、海啸、飓风、水旱灾、泥石流等)频繁发生,给人类带来极大的生命和财产损失,损失爆发的频率和严重程度以惊人的速度上升.由此引发的巨额保险赔付让传统的保险经营方式承受着极大的挑战,制约了保险业的发展.巨灾期权是一种保险风险转移的金融工具,他利用风险证券化将保险市场与证券市场有效结合,用资本市场的实力来分散(再)保险公司的巨灾风险,使金融、保险实现一体化.尽管巨灾期权或巨灾股票期权深受保险业和投资者的喜爱,但是他们并没有在市场上很好的发展起来,究其原因主要是难以准确定价期权合约,以及供投资者选择的证券化产品数量不足.基于此,本文通过引入一类新型的巨灾任选股票期权,并研究其定价与风险管理问题,主要内容有：第二章在常数利率条件下假设巨灾损失总额满足复合Poisson过程,以及市场股票价格满足几何布朗运动的情形下,研究巨灾简单任选期权和复杂任选期权的定价,给出了他们的定价公式和对冲避险策略.在假定巨灾损失额服从正态分布的条件下进一步给出巨灾任选期权的评价,以及数值计算了风险发生频率入,巨灾损失参数θ,δ对期权合约的影响.第三章在随机利率条件下研究巨灾简单任选期权和复杂任选期权的定价问题,应用远期测度变换方法给出了巨灾任选股票期权的显示解,并在利率满足Vasicek模型下分析了利率模型中各参数值变动对期权价格的影响.第四章总结了本文的主要工作及有待进一步研究的问题.更多还原

【Abstract】 The catastrophe risks are generated by these events of natural catastrophe which are of sudden, nopredicting, noavoiding and have great harmfulness. In recent decades,the worldwide natural dis-asters (like earthquake, tsunami, hurricane, flood drought and debris flows etc.)occur frequently, and cause huge loss of lives and property. The occurred frequency of loss and severity of the catas-trophe are increasing wonderfully. Caused by the huge insurance compensation let the traditional insurance management way bear the great challenge, and restrict the development of the insurance industry. Catastrophe option is a financial instrument for shifting the insurance risks, combines the insurance market with stock market effectively by securitizing the catastrophe risks,and spreads the catastrophe risks of insurance or reinsurance industry by means of the capital market. These result in integration between finance and insurance.Although the catastrophe options or the catastrophe stock options are favourited by the in-surance industry and many investors, they are not very well developed in the market. The main reasons include the difficult pricing the option accurately and the short of amount of securitised products for investor choosing. Based on these mentioned above,an new product of catastrophe option, called by catastrophe chooser option Written on stock whose pricing and hedging are con-sidered in this thesis. Main contributions are as follows:In chapter2, the pricings of both European catastrophe simple chooser option and complex chooser option are considered under the stock’s price following the diffusion model and constant interest rate framework with the catastrophe losses generated by a compound Poisson process. The closed-form solutions of the price and hedging strategy are obtained. Furthermore, the pricing closed-form solution of the European chooser options are also gained and some numerical exam-ples such as the affect of the parameters λ, θ,δ to the option are provided under the size of the losses satisfying the normal distribution.In chapter3,we derived the analytic price formulas for the European catastrophe chooser op-tions within the stochastic interest rate framework by using forward martingale method, and the explicit solutions of the chooser options are obtained. Some behaviours of parameters in the Va-sicek model are analyzed with numerical examples.Main conclusions and the further research works are summarized in chapter4.更多还原