蒙特卡罗方法在三类金融衍生产品定价中的应用
发布时间：2018-08-06 20:01
【摘要】：金融衍生产品的定价和对冲、风险管理、最优投资组合以及模型校正是金融业界最关心的四个问题，其中金融衍生产品的定价更是重中之重。Black和Scholes关于期权定价模型的诞生使得衍生品定价的研究发生了历史性的突破，引起了广泛的关注。在当今金融市场中，衍生产品的种类繁多，除了标准的欧式期权和美式期权，还不断涌现出了大量的新型期权和其它金融衍生工具，这为金融衍生产品的定价工作带来了巨大的挑战。 定价的难度从本质上看是由较高的维度带来的，导致相关的金融衍生产品的定价模型无法得到解析解，需要借助数值方法来解决。蒙特卡罗(Monte Carlo)方法是一种基于随机数的数值模拟方法，该方法收敛的阶与问题的维数无关，这使得Monte Carlo方法成为计算高维金融衍生产品定价问题的重要工具。随着Monte Carlo方法的发展，众多方差缩小技术也得到了广泛应用，克服了MonteCarlo方法收敛速度较慢的缺陷。本文将从外汇期权、一篮子期权、信用违约互换(CDS)三个方面，研究Monte Carlo方法在金融衍生产品定价中的应用。总共分为六章： 第一章，前言部分，综述了本文选题的背景和意义，并介绍了国内外相关研究的现状和本文所研究的内容。 第二章，概述了Monte Carlo方法的主要思想和基本原理，介绍了它在金融衍生产品定价问题研究中的应用及其优势，然后简要介绍了几种常用的方差缩小技术。 第三章，利用鞅表示性质建立了利率和汇率波动率均为随机情形下算术平均亚式外汇期权的定价模型。由于所得方程没有显式解，运用Monte Carlo方法并结合控制变量方差减小技术进行模拟分析，数值试验表明有效地减小了模拟方差，并得到了该期权定价问题的数值结果。 第四章，在随机利率满足Vasicek模型的假设下，运用多元均值控制变量蒙特卡罗(MMC)方法对一篮子算术平均亚式期权定价问题进行模拟分析，有效地减小了模拟误差，得到了该期权定价问题的数值结果。 第五章，研究了交易对手具有多信用等级的信用违约互换的定价问题。考虑交易对手的违约强度随着信用等级的迁移而变化，同时影响参考公司的违约强度，，构建了基于信用等级迁移的违约传染模型。通过分析不同违约情况下的现金流建立了CDS合约价值的定价模型，利用蒙特卡罗方法求得其数值解并计算CVA。 第六章，总结了本文研究的主要内容，并给出了不足之处和有待深入研究的问题。
[Abstract]:The pricing and hedging of financial derivatives, risk management, optimal portfolio and model correction are the four most concerned issues in the financial sector. Among them, the pricing of financial derivatives is the most important. Black and Scholes on option pricing model of the birth of the derivatives pricing research has made a historic breakthrough, caused widespread concern. In today's financial market, there are many kinds of derivative products. In addition to the standard European options and American options, a large number of new options and other financial derivatives have been emerging. This brings great challenges to the pricing of financial derivatives. In essence, the difficulty of pricing is brought by the higher dimension, which leads to the pricing model of related financial derivatives can not be solved analytically, so it needs to be solved by numerical method. Monte Carlo (Monte Carlo) method is a numerical simulation method based on random numbers. The order of convergence of the method is independent of the dimension of the problem, which makes the Monte Carlo method become an important tool to calculate the pricing problem of high-dimensional financial derivatives. With the development of Monte Carlo method, many variance narrowing techniques have been widely used, which overcomes the slow convergence speed of MonteCarlo method. This paper will study the application of Monte Carlo method in the pricing of financial derivatives from three aspects: foreign exchange options, basket options and credit default swaps (CDS). There are six chapters altogether: the first chapter, the preface part, summarizes the background and significance of this paper, and introduces the current situation of domestic and foreign related research and the content of this paper. In the second chapter, the main idea and basic principle of Monte Carlo method are summarized, and its application and advantages in the research of financial derivative pricing problem are introduced. Then, several commonly used variance narrowing techniques are briefly introduced. In the third chapter, the pricing model of arithmetic average Asian foreign exchange option is established by using martingale representation property under the condition that interest rate and exchange rate volatility are both stochastic. Because there is no explicit solution to the obtained equation, the Monte Carlo method and the control variable variance reduction technique are used to simulate and analyze. The numerical experiments show that the simulated variance is reduced effectively, and the numerical results of the option pricing problem are obtained. In chapter 4, under the assumption that the stochastic interest rate satisfies the Vasicek model, the Monte Carlo (MMC) method is used to simulate and analyze a basket of arithmetic average Asian option pricing problem, which effectively reduces the simulation error. The numerical results of the option pricing problem are obtained. In chapter 5, we study the pricing of credit default swaps with multiple credit rating. Considering that the default intensity of counterparty varies with the credit grade transfer and affects the default intensity of the reference company, a default contagion model based on credit grade transfer is constructed. The pricing model of CDS contract value is established by analyzing the cash flow in different default cases, and the numerical solution is obtained by Monte Carlo method. In the sixth chapter, the main contents of this paper are summarized, and the shortcomings and problems to be further studied are given.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224
本文编号：2168836
[Abstract]:The pricing and hedging of financial derivatives, risk management, optimal portfolio and model correction are the four most concerned issues in the financial sector. Among them, the pricing of financial derivatives is the most important. Black and Scholes on option pricing model of the birth of the derivatives pricing research has made a historic breakthrough, caused widespread concern. In today's financial market, there are many kinds of derivative products. In addition to the standard European options and American options, a large number of new options and other financial derivatives have been emerging. This brings great challenges to the pricing of financial derivatives. In essence, the difficulty of pricing is brought by the higher dimension, which leads to the pricing model of related financial derivatives can not be solved analytically, so it needs to be solved by numerical method. Monte Carlo (Monte Carlo) method is a numerical simulation method based on random numbers. The order of convergence of the method is independent of the dimension of the problem, which makes the Monte Carlo method become an important tool to calculate the pricing problem of high-dimensional financial derivatives. With the development of Monte Carlo method, many variance narrowing techniques have been widely used, which overcomes the slow convergence speed of MonteCarlo method. This paper will study the application of Monte Carlo method in the pricing of financial derivatives from three aspects: foreign exchange options, basket options and credit default swaps (CDS). There are six chapters altogether: the first chapter, the preface part, summarizes the background and significance of this paper, and introduces the current situation of domestic and foreign related research and the content of this paper. In the second chapter, the main idea and basic principle of Monte Carlo method are summarized, and its application and advantages in the research of financial derivative pricing problem are introduced. Then, several commonly used variance narrowing techniques are briefly introduced. In the third chapter, the pricing model of arithmetic average Asian foreign exchange option is established by using martingale representation property under the condition that interest rate and exchange rate volatility are both stochastic. Because there is no explicit solution to the obtained equation, the Monte Carlo method and the control variable variance reduction technique are used to simulate and analyze. The numerical experiments show that the simulated variance is reduced effectively, and the numerical results of the option pricing problem are obtained. In chapter 4, under the assumption that the stochastic interest rate satisfies the Vasicek model, the Monte Carlo (MMC) method is used to simulate and analyze a basket of arithmetic average Asian option pricing problem, which effectively reduces the simulation error. The numerical results of the option pricing problem are obtained. In chapter 5, we study the pricing of credit default swaps with multiple credit rating. Considering that the default intensity of counterparty varies with the credit grade transfer and affects the default intensity of the reference company, a default contagion model based on credit grade transfer is constructed. The pricing model of CDS contract value is established by analyzing the cash flow in different default cases, and the numerical solution is obtained by Monte Carlo method. In the sixth chapter, the main contents of this paper are summarized, and the shortcomings and problems to be further studied are given.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224
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