双货币模型下资产价格带跳的期权定价

发布时间：2018-01-02 02:17

本文关键词：双货币模型下资产价格带跳的期权定价　出处：《哈尔滨师范大学》2013年硕士论文　论文类型：学位论文

【摘要】：本文主要研究双币种模型下资产价格带跳的期权定价问题,当金融市场中风险资产的价格出现跳跃的时候,原有的Black-Scholes模型已经不再适用.文中讨论了欧式期权及美式期权的定价. 本文中欧式期权的定价是在风险资产价格的跳跃服从Poisson过程且跳跃幅度为常数的假定条件下,利用多因子的Girsanov定理及资产价格带跳的Girsanov定理,构造出与原市场测度P等价的测度Q并且证明了测度Q是风险中性的,进而运用期权定价的鞅方法,得出模型下欧式期权定价的显示表达式. 美式期权的定价则不能得到显式表达式,为计算简便,模型与欧式期权相比稍有变化,但本质相同.由于单个风险资产的跳跃对于整个市场的影响是微乎其微的,因此,需要讨论资产价格的跳跃风险是否被计算在期权价格之中,进而采取不同的-对冲策略,通过期权定价的偏微分方法,得到美式期权价格所满足的自由边界问题. 当资产价格发生跳跃或其他突发事件发生时,可以用此模型来对冲风险,具有一定的现实意义.
[Abstract]:This paper mainly studies the option pricing problem of asset price with jump under the dual currency model, when the price of risky assets jumps in the financial market. The original Black-Scholes model is no longer applicable. The pricing of European and American options is discussed in this paper. In this paper, the pricing of European options is under the assumption that the price of risky assets jumps from the Poisson process and the jump amplitude is constant. By using the Girsanov theorem of multiple factors and the Girsanov theorem of asset price with jump, we construct measure Q which is equivalent to the original market measure P and prove that measure Q is risk-neutral. Then, using the martingale method of option pricing, the display expression of European option pricing under the model is obtained. The pricing of American option can not get an explicit expression. In order to calculate easily, the model is slightly different from that of European option. However, the essence is the same. Because the jump of individual risk assets has little effect on the whole market, it is necessary to discuss whether the jump risk of asset price is calculated in the option price. Then we adopt different hedging strategies and obtain the free boundary problem of American option price by using the partial differential method of option pricing. This model can be used to hedge the risk when the asset price jumps or other emergencies occur, which has certain practical significance.
【学位授予单位】：哈尔滨师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224

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