蒙特卡罗模拟法和拟蒙特卡罗模拟法在期权定价问题中的对比研究

发布时间：2018-01-12 01:36

本文关键词：蒙特卡罗模拟法和拟蒙特卡罗模拟法在期权定价问题中的对比研究　出处：《复旦大学》2013年硕士论文　论文类型：学位论文

【摘要】：期权以及其他金融衍生产品在金融市场中变得越来越重要。随着我国金融市场创新力度的加大,在商品期货、股指期货之后,期权也将要推出交易。期权定价问题就显得尤为重要,期权的合理定价不仅能够使交易市场稳步有序,更能给投资者的投资决策提供重要的信息。期权定价主要有三种方法：偏微分方程法、鞅方法以及数值方法,蒙特卡罗方法就是数值方法中的一种。蒙特卡罗方法是一种向后计算方法,在解决路径依赖的期权定价问题上十分有效。而收敛速度慢、模拟精度不高以及计算效率较低成为了蒙特卡罗方法的不足。拟蒙特卡罗方法也叫低差异方法是对蒙特卡罗方法的一种改进,拟蒙特卡罗方法的收敛率为O(1/n),比传统蒙特卡罗方法O(1/√n)的收敛速度快得多,提高了模拟效率与精度。本文研究蒙特卡罗方法以及拟蒙特卡罗方法生成的随机数序列的性质,以Halton序列为例,通过仿真模拟,对比了蒙特卡罗方法以及拟蒙特卡罗方法在期权定价上的精确性以及模拟效率,并以BS期权定价公式算出的期权理论价格作为参考,证实了拟蒙特卡罗方法在随机数序列生成以及期权定价上的优势。并且应用模拟方法对路径依赖的特种期权进行定价,从模拟结果中分析了特种期权的一些性质。本文的创新点包括：1)用蒙特卡罗方法以及拟蒙特卡罗方法对期权定价,并且在Matlab软件上编写所有程序做实证分析；2)研究拟蒙特卡罗Halton序列的性质以及其生成的拟随机数的特点；3)对蒙特卡罗以及拟蒙特卡罗方法在期权定价问题上进行仿真模拟,以及对比研究,证明拟蒙特卡罗方法的优势。
[Abstract]:Options and other financial derivatives are becoming more and more important in the financial market. With the increase of innovation in our financial market, after commodity futures, stock index futures. The issue of option pricing is especially important. The reasonable pricing of options can not only make the trading market orderly but also provide important information for investors to make investment decisions. There are three methods for option pricing: partial differential equation method martingale method and numerical method. Monte Carlo method is one of the numerical methods. Monte Carlo method is a backward calculation method. It is very effective in solving the path-dependent option pricing problem, but the convergence rate is slow. The deficiency of Monte Carlo method is low simulation precision and low calculation efficiency. Quasi-Monte Carlo method, also called low difference method, is an improvement on Monte Carlo method. The convergence rate of the quasi-Monte Carlo method is 1 / n ~ (-1), which is much faster than that of the traditional Monte-Carlo method, and the efficiency and accuracy of the simulation are improved. In this paper, we study the properties of random number sequences generated by Monte Carlo method and quasi Monte Carlo method. Taking Halton sequences as an example, we simulate them by simulation. The accuracy and simulation efficiency of Monte-Carlo method and quasi-Monte Carlo method in option pricing are compared, and the theoretical price of option calculated by BS option pricing formula is taken as reference. The advantages of quasi-Monte Carlo method in generating random number sequences and pricing options are confirmed, and the path-dependent special options are priced by simulation method. Some properties of special options are analyzed from the simulation results. The innovations of this paper include: (1) pricing options with Monte Carlo method and quasi Monte Carlo method, and writing all programs on Matlab software for empirical analysis; 2) the properties of quasi Monte Carlo Halton sequences and the characteristics of their generated quasi random numbers are studied. 3) the paper simulates and compares the Monte Carlo and quasi Monte Carlo methods in option pricing problem, and proves the advantage of quasi Monte Carlo method.
【学位授予单位】：复旦大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.9

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