【摘要】：金融衍生產(chǎn)品的定價和對沖、風(fēng)險管理、最優(yōu)投資組合以及模型校正是金融業(yè)界最關(guān)心的四個問題，其中金融衍生產(chǎn)品的定價更是重中之重。Black和Scholes關(guān)于期權(quán)定價模型的誕生使得衍生品定價的研究發(fā)生了歷史性的突破，引起了廣泛的關(guān)注。在當(dāng)今金融市場中，衍生產(chǎn)品的種類繁多，除了標(biāo)準(zhǔn)的歐式期權(quán)和美式期權(quán)，還不斷涌現(xiàn)出了大量的新型期權(quán)和其它金融衍生工具，這為金融衍生產(chǎn)品的定價工作帶來了巨大的挑戰(zhàn)。 定價的難度從本質(zhì)上看是由較高的維度帶來的，導(dǎo)致相關(guān)的金融衍生產(chǎn)品的定價模型無法得到解析解，需要借助數(shù)值方法來解決。蒙特卡羅(Monte Carlo)方法是一種基于隨機(jī)數(shù)的數(shù)值模擬方法，該方法收斂的階與問題的維數(shù)無關(guān)，這使得Monte Carlo方法成為計算高維金融衍生產(chǎn)品定價問題的重要工具。隨著Monte Carlo方法的發(fā)展，眾多方差縮小技術(shù)也得到了廣泛應(yīng)用，克服了MonteCarlo方法收斂速度較慢的缺陷。本文將從外匯期權(quán)、一籃子期權(quán)、信用違約互換(CDS)三個方面，研究Monte Carlo方法在金融衍生產(chǎn)品定價中的應(yīng)用�？偣卜譃榱拢� 第一章，前言部分，綜述了本文選題的背景和意義，并介紹了國內(nèi)外相關(guān)研究的現(xiàn)狀和本文所研究的內(nèi)容。 第二章，概述了Monte Carlo方法的主要思想和基本原理，介紹了它在金融衍生產(chǎn)品定價問題研究中的應(yīng)用及其優(yōu)勢，然后簡要介紹了幾種常用的方差縮小技術(shù)。 第三章，利用鞅表示性質(zhì)建立了利率和匯率波動率均為隨機(jī)情形下算術(shù)平均亞式外匯期權(quán)的定價模型。由于所得方程沒有顯式解，運用Monte Carlo方法并結(jié)合控制變量方差減小技術(shù)進(jìn)行模擬分析，數(shù)值試驗表明有效地減小了模擬方差，并得到了該期權(quán)定價問題的數(shù)值結(jié)果。 第四章，在隨機(jī)利率滿足Vasicek模型的假設(shè)下，運用多元均值控制變量蒙特卡羅(MMC)方法對一籃子算術(shù)平均亞式期權(quán)定價問題進(jìn)行模擬分析，有效地減小了模擬誤差，得到了該期權(quán)定價問題的數(shù)值結(jié)果。 第五章，研究了交易對手具有多信用等級的信用違約互換的定價問題�？紤]交易對手的違約強(qiáng)度隨著信用等級的遷移而變化，同時影響參考公司的違約強(qiáng)度，，構(gòu)建了基于信用等級遷移的違約傳染模型。通過分析不同違約情況下的現(xiàn)金流建立了CDS合約價值的定價模型，利用蒙特卡羅方法求得其數(shù)值解并計算CVA。 第六章，總結(jié)了本文研究的主要內(nèi)容，并給出了不足之處和有待深入研究的問題。
[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.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F830.9;F224

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