单因子利率模型下的外汇期权定价

发布时间：2018-01-11 17:45

本文关键词：单因子利率模型下的外汇期权定价　出处：《西南财经大学》2012年硕士论文　论文类型：学位论文

【摘要】：金融衍生品定价是金融领域内的一大重要问题,实际应用价值很大,同时又有极大的理论意义。外汇期权即是一种较为复杂的金融衍生工具,在我国市场上也是新近出现。我国现有的外汇期权产品都比较简单,对其主要是处在摸索阶段,特别是距发达国家成熟的外汇期权体系还相差甚远,所以此时对外汇期权的定价问题进行一些探索和研究是很有必要的。本文即是研究了单因子利率模型下欧式外汇期权的合理定价问题。期权是一种金融衍生产品,它的定价模型主要取决于原生资产的价格演化模型。在连续时间情形下,原生资产的价格演化可以表述为一个随机微分方程,作为原生资产衍生物的期权的定价问题在此基础上就可以变为一个偏微分方程的定解问题。因此,研究期权定价的主要思路便是把偏微分方程作为工具,利用偏微分方程的理论和方法,建立起期权定价的数学模型,就能得出期权的定价公式,还可对期权的价格结构做定性分析。本文即是沿着这个思路展开的。首先,在单因子利率模型下,给出了外汇期权的相关假设条件,再得到在假设条件下的欧式外汇期权所需满足的偏微分方程,此方程主要是运用鞅表示定理得到的。其次,就是对得到的偏微分方程进行求解,此方程为三维形式,直接求解较复杂,本文就先利用远期变量变换降低了偏微分方程状态空间的维数,将方程转化为普通的一维形式的边界问题。再次,得出期权的定价公式。这里,运用B-S公式就解出了相应的欧式看涨和看跌外汇期权的显式解。最后,本文还根据得出的欧式外汇期权的定价公式对影响其价格的因素进行了敏感性分析,联系实际,从侧面佐证了定价公式的正确性。
[Abstract]:The pricing of financial derivatives is an important problem in the field of finance, which has great practical application value and great theoretical significance. Foreign exchange option is a more complex financial derivative instrument. The existing foreign exchange option products in China are relatively simple, mainly in the exploratory stage, especially far from the mature foreign exchange options system in developed countries. Therefore, it is necessary to explore and study the pricing of foreign exchange options. In this paper, we study the rational pricing of European foreign exchange options under the single-factor interest rate model. Option is a kind of financial derivative, its pricing model mainly depends on the price evolution model of the original asset. In the case of continuous time, the price evolution of the original asset can be expressed as a stochastic differential equation. On this basis, the pricing problem of options as a derivative of original assets can be transformed into a definite solution of partial differential equation. Therefore, the main idea of studying option pricing is to use partial differential equation as a tool. By using the theory and method of partial differential equation, the mathematical model of option pricing can be established and the option pricing formula can be obtained. The price structure of options can also be qualitatively analyzed. This paper starts with this idea. First of all, under the single-factor interest rate model, the relevant assumptions of foreign exchange options are given. Then we obtain the partial differential equation of the European foreign exchange option under the hypothetical condition. This equation is mainly obtained by using martingale representation theorem. Secondly, the obtained partial differential equation is solved. This equation is a three-dimensional form, the direct solution is more complex, this paper first use the forward variable transformation to reduce the dimension of the state space of partial differential equations, and transform the equation into the ordinary one-dimensional boundary problem. Here, using B-S formula to solve the corresponding European call and put foreign exchange options explicit solution. Finally. According to the European foreign exchange option pricing formula, this paper also analyzes the sensitivity of the factors affecting the price of the foreign exchange option, connecting with the practice, it proves the correctness of the pricing formula from the side.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F832.6;F224

【引证文献】