巨灾权益连结卖权定价模型研究:基于随机波动率与随机利率条件  

Pricing model of catastrophe equity put option:Based on the conditions of stochastic volatility and stochastic interest rate

作　　者：柏满迎[1] 郝军章 翟嘉 赵越强 BAI Man-ying;HAO Jun-zhang;ZHAI Jia;ZHAO Yue-qiang(School of Economics and Management,Beihang University,Beijing 100191,China)

机构地区：[1]北京航空航天大学经济管理学院

出　　处：《管理工程学报》2019年第3期170-178,共9页Journal of Industrial Engineering and Engineering Management

基　　金：国家自然科学基金面上资助项目(71571007、71371021);国家自然科学基金重点资助项目(71333014)

摘　　要：巨灾权益连结卖权作为一种新型复合期权,它能够保证保险公司不会同时承受巨灾导致的赔付风险与公司股价下跌造成的流动性风险,其引发了广大学者的研究。但现有卖权定价研究仍存在一些不足,如未考虑随机波动率的情况、没有综合考虑随机利率和随机波动率的影响、巨灾对股价影响函数的设定不合理、未确定巨灾风险的等价鞅测度等。为了克服这些不足,本文在研究巨灾权益连结卖权定价问题时,考虑了随机利率和随机波动率影响因素,利用Vasicek模型刻画利率期限结构,同时假设单位时间内巨灾损失对股价收益率影响是恒定的,提出了一种更加合理的巨灾损失影响函数形式。在此基础上,本文放宽了巨灾风险分布不受测度变换的假设,确定了受巨灾影响的股价过程的等价鞅测度,从而得到了巨灾权益连结卖权的定价公式。最后,文章运用蒙特卡罗模拟的方法对巨灾权益连结卖权价值的影响因素进行了敏感性分析,以验证本文模型的合理性。The catastrophe equity put option is a kind of compound option, which enables the buyer (usually an insurance company) to sell a certain share of the convertible stock to the issuer at the predetermined price. However, this right can be executed if the accumulated loss exceeds a certain amount. The catastrophe equity put option is designed to ensure that an insurer would not suffer from enormous compensation or great fall in share value when a catastrophe occurs. From the mechanism of this put option, it is not difficult to see that the benefits not only depend on the stock prices but also depend on the cumulative loss. This new-styled option attracts great attention from the researchers. There are still some aspects to be improved in the current research. Firstly, the volatility is considered as constant and invariant, which is not in accord with reality. Secondly, the impact of stochastic interest rate and stochastic volatility are not considered at the same time. Thirdly, the influence function of catastrophe is set unreasonable and the formulation to reflect the relationship between share value and losses is not reasonable. Besides, in current research distribution of catastrophic losses is assumed to be invariant in different measures, which also deviates from the actual situation. Finally, the equivalent martingale measure of the stock price affected by catastrophe risk is not yet determined. In our research, because the price of catastrophe equity put option is more sensitive to interest rate, and volatility rate, the combination of both rates can depict the randomness effectively. We introduce the Vasicek model to solve the problem of interest rate term structure and study the problem of pricing the double trigger catastrophe equity put option with stochastic volatility and stochastic interest rate in order to improve the precision of option pricing model. In addition, there are also many defects in setting catastrophic influence function and parameters. Existing researches cannot propose a reasonable cat

关 键 词：随机波动率 随机利率 巨灾权益连结卖权 等价鞅测度 

分 类 号：F830[经济管理—金融学]