障碍期权的模糊数定价

发布时间：2018-06-02 16:04

本文选题：障碍期权 + 模糊数　；参考：《中国矿业大学》2014年硕士论文

【摘要】：障碍期权是一种路径依赖期权,它的收益取决于标的资产价格在持有期内是否触碰到障碍值.障碍期权的期权金低于欧式期权,并且障碍期权合约灵活地表现了投资者的主观意愿,因此深受投资者喜爱.在期权定价过程中,标的资产价格的不确定性包括随机性和模糊性,而一般的期权定价模型只考虑其随机性,对模糊性却研究甚少.本文建立的期权定价模型既考虑了标的资产价格的随机性,又考虑了其模糊性. 本文主要研究向下敲入、敲出看涨期权在模糊环境下的定价问题.首先,将到期日的股票价格模糊化,得到新的支付函数.然后,运用风险中性定价原理和Girsanov定理,推导股票价格服从几何布朗运动时,向下敲入、敲出看涨期权的定价公式.最后,进一步研究股票价格服从跳扩散过程时,向下敲入、敲出看涨期权的模糊理论定价.具体工作如下: (1)假设股票价格服从几何布朗运动,将到期日的股票价格用梯形模糊数表示,使得期权在到期日的损益模糊化.然后运用风险中性定价原理和Girsanov定理,求解欧式看涨期权以及向下敲入、敲出看涨期权在模糊环境下的定价公式,并给出敲入、敲出期权与欧式期权价值之间的关系.最后通过数值试验分析期权价值与股票价格的关系以及新的定价模型的有效性,并与B-S定价公式进行比较. (2)假设股票价格服从跳扩散过程,运用模糊理论将到期日的股票价格模糊化,再结合风险中性定价原理和Girsanov定理,研究欧式看涨期权以及向下敲入、敲出看涨期权在跳扩散过程下的定价问题,得到了无穷级数形式的定价公式,并证明了该定价公式是收敛的.最后通过数值试验分析期权价值与股票价格的关系,并与跳扩散过程下的一般定价公式进行比较.
[Abstract]:Obstacle option is a path dependent option, and its income depends on whether the underlying asset price touches the barrier value in the holding period. The option gold of barrier option is lower than that of European option, and obstacle option contract flexibly expresses the subjective will of investors, so it is loved by investors. In the process of option pricing, the uncertainty of underlying asset price includes randomness and fuzziness, but the general option pricing model only considers its randomness, but there is little research on fuzziness. The option pricing model in this paper not only considers the randomness of underlying asset price, but also considers its fuzziness. This paper mainly studies the pricing of call option in fuzzy environment. Firstly, the stock price of maturity date is blurred and a new payment function is obtained. Then, by using the risk-neutral pricing principle and Girsanov theorem, the pricing formula of call option is derived when stock price is driven by geometric Brownian motion. Finally, this paper further studies the fuzzy theory pricing of call option when stock price spreads from jump to diffusion, knocks down and knocks out call options. The specific work is as follows: 1) assuming that stock price moves from geometric Brownian motion, the stock price on maturity date is expressed as trapezoidal fuzzy number, which makes the gains and losses of option on maturity date fuzzy. Then the risk neutral pricing principle and Girsanov theorem are used to solve the European call option and down knock in, and the pricing formula of call option in fuzzy environment is given, and the relationship between the value of call option and European option is given. Finally, the relationship between option value and stock price and the validity of the new pricing model are analyzed by numerical experiments, and compared with B-S pricing formula. (2) assuming the process of stock price diffusion from jump to diffusion, the stock price of maturity date is fuzzy by using fuzzy theory, and combining with risk neutral pricing principle and Girsanov theorem, the paper studies European call options and knocks down. In this paper, the pricing problem of call option in the process of jump diffusion is discussed, and the pricing formula of infinite series is obtained, and it is proved that the formula is convergent. Finally, the relationship between option value and stock price is analyzed by numerical experiments, and compared with the general pricing formula in the process of jump diffusion.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F830.91;O159

【参考文献】