外汇期权定价问题的研究

发布时间：2018-01-01 13:23

本文关键词：外汇期权定价问题的研究　出处：《燕山大学》2013年硕士论文　论文类型：学位论文

【摘要】：在1973年Black和Scholes提出了Black-Scholes期权定价模型。把Black-Scholes定价模型应用于外汇期权时即熟知的—G-K模型。著名Black-Scholes期权公式在金融衍生工具定价研究领域占有非常重要的位置，然而Black-Scholes期权公式在实际应用中存在缺陷，主要是股价回报率的波动率假设为常数。而实际数据表明，股价回报率分布呈现两个显著特点：尖峰和厚尾，不符合标准正态分布的特征。因此人们开始研究更适合实际市场的股价行为模型，基于此，本文做了如下工作：首先，对于经典的外汇期权模型—G-K模型，采用了随机微分方程法和保险精算法两种方法进行了证明。对于随机微分方程法，先求出外汇期权V所要满足的偏微分方程，对该偏微分方程在有效期内求定解问题，再进行变换，然后应用一般情况下的Black—Scholes期权定价模型就可证明出结果。对于保险精算方法，利用期权在有效期内所承担风险的保障费即所求期权的价格的原理，以二叉树模型为基准，结合外汇期权的特点，根据无套利原则和风险中性原则，推导出外汇期权的二叉树模型。其次，分析了外汇期权的二叉树模型和G-K模型之间存在的联系，利用风险中性原则法、中心极限定理以及二项式与二叉树模型的相关性质，在选择适当的上涨因子和下跌因子及上涨概率时，可用二叉树模型逼近经典外汇期权定价模型，并证明出了这个联系。最后，在前人研究的基础上对G-K模型做了一些调整，建立了正态跳扩散模型并将其应用于外汇期权的定价。在外汇模型假设和正态跳扩散模型的假设下，利用在一般均衡市场理论下的概率测度推导出了正态跳扩散模型的外汇期权定价模型。还给出了此模型下的期货期权的定价模型公式，，并证明了结论。
[Abstract]:In 1973, Black and Scholes put forward the Black-Scholes option pricing model. Black-Scholes pricing model was applied to foreign exchange options. Known -G-K model. The famous Black-Scholes option formula plays a very important role in the field of financial derivatives pricing. However, the Black-Scholes option formula has some defects in practical application, mainly because the volatility of the return on stock price is assumed to be constant. The distribution of return on stock price presents two remarkable characteristics: peak and thick tail, which do not accord with the characteristics of standard normal distribution. Therefore, people begin to study the stock price behavior model which is more suitable for the actual market. This paper has done the following work: First of all, for the classical foreign exchange options model-G-K model, the stochastic differential equation method and the actuarial insurance method are used to prove. For the stochastic differential equation method. The partial differential equation of foreign exchange option V is obtained first, and then the solution of the partial differential equation is obtained within the validity period, and then the transformation is carried out. Then the Black-Scholes option pricing model can be used to prove the result. Using the principle of the guarantee cost of the risk that the option bears during the period of validity, taking the binary tree model as the benchmark, combining the characteristics of the foreign exchange option, according to the principle of no arbitrage and risk neutrality. The binary tree model of foreign exchange options is derived. Secondly, the relationship between binomial tree model and G-K model of foreign exchange option is analyzed. The risk neutral principle, the central limit theorem and the properties of binomial and binomial tree model are used. When we select the appropriate rising factor, falling factor and rising probability, we can approach the classical foreign exchange option pricing model by using the binary tree model, and prove this connection. Finally, the G-K model is adjusted on the basis of previous studies, and the normal jump diffusion model is established and applied to the pricing of foreign exchange options, under the assumption of the foreign exchange model and the normal jump diffusion model. By using the probability measure under the general equilibrium market theory, the foreign exchange option pricing model of normal jump diffusion model is derived, the formula of futures option pricing model under this model is given, and the conclusion is proved.
【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224

【引证文献】