随机利率下具有幂型支付的重置期权定价

发布时间：2018-01-22 14:38

本文关键词： 单点重置期权多点重置期权幂型支付随机利率扩展Vasicek模型鞅方法　出处：《华东师范大学》2012年硕士论文　论文类型：学位论文

【摘要】：随着金融市场的发展与完善,各种依赖路径的期权层出不穷.重置期权作为一类典型的路径依赖期权,自20世纪90年代开始活跃于证券交易市场.重置的看涨期权是指在某一特定时刻,当标的资产价格低于初始敲定价格时,则将敲定价格重置为该时刻的标的资产价格.在期权定价过程中,无风险利率的结构起着关键作用.另一方面,幂型支付形式有助于投资者获得更大的收益,从而改变收益结构.文章中假设无风险利率服从扩展Vasicek模型,重点讨论了幂型支付形式下的重置期权的定价.首先研究了在风险中性测度下的传统单点重置期权在幂型支付下的情形,通过定义两个新的测度并由Girsanov定理得到新的测度下的布朗运动,运用鞅定价的方法、布朗运动的正交分解以及贝叶斯法则计算得到期权价格的显式解：而后进一步推导出具有多个重置点情形下的定价公式,运用以上定义的两个等价鞅测度以及多维正态分布的运算得到不同时刻的价格.
[Abstract]:With the development and improvement of financial market, a variety of path-dependent options emerge in endlessly. Replacement options as a typical type of path-dependent options. A call option that has been active in the stock market since 1990s. A reset call option is defined as a call option when the underlying asset price is lower than the initial fixed price at a particular time. The structure of risk-free interest rates plays a key role in the option pricing process. On the other hand, power-type payment forms help investors to achieve greater returns. In this paper, the risk-free interest rate is assumed to be based on the extended Vasicek model. This paper focuses on the pricing of replacement options in the form of power-type payment. Firstly, the case of traditional single-point replacement options under risk-neutral measure under power-type payment is studied. By defining two new measures and obtaining the Brownian motion under the new measure by Girsanov theorem, the method of martingale pricing is used. The orthogonal decomposition of the Brownian motion and the Bayesian rule calculate the explicit solution of the option price. Then the pricing formula with multiple reset points is derived. The price at different times is obtained by using the two equivalent martingale measures defined above and the operation of multidimensional normal distribution.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.9;F224

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