对一篮子期权定价模型的研究

发布时间：2018-01-04 03:35

本文关键词：对一篮子期权定价模型的研究　出处：《燕山大学》2014年硕士论文　论文类型：学位论文

【摘要】：期权是一种金融衍生品，是建立在基础资产之上的。期权是市场经济中不可或缺的一部分，提供了新的投资方式。期权在国外已得到广泛应用，国内各大交易所今年陆续开展期权的仿真交易大赛。随着期权的发展，期权定价理论也成为现代金融学的核心问题之一。一篮子期权是一种新型期权，是多种标的资产期权的组合投资，起到不同于单一期权的套期保值效果。一篮子期权是应投资者对投资组合分散化日益增长的要求而产生的。它为投资者提供了更广阔的投资空间，开阔了投资思路。因此一篮子期权的定价问题也成为一篮子期权在实践过程中的关键问题。论文旨在研究一篮子期权在随机波动率下的定价模型以及定价公式，并用蒙托卡罗模拟一篮子期权，，找到模型的数值解。论文运用历史研究法和举例研究法，对一篮子期权进行初步研究。论文首先研究了经典的Black-Scholes期权定价模型，在该定价模型的假设基础上，研究多资产期权的定价模型以及多资产期权定价的求解方法，从而得到一篮子期权的定价模型及定价公式；其次将随机波动模型加入到一篮子期权定价模型中，得到随机波动率下的一篮子期权定价公式；最后对蒙托卡罗模拟方法的方差缩减技术进行探讨，并将控制变量技术应用到一篮子期权定价的蒙托卡罗模拟中。
[Abstract]:Option is a kind of financial derivative, which is based on basic assets. Option is an indispensable part of market economy and provides a new way of investment. Options have been widely used in foreign countries. With the development of options, option pricing theory has become one of the core problems in modern finance. A basket option is a new type of option, which is a combination of various underlying asset options. A basket of options is produced in response to the growing demand of investors for diversification of the portfolio. It provides investors with a broader investment space. Therefore, the pricing of a basket of options has become a key issue in the practice of a basket of options. The purpose of this paper is to study the pricing model and pricing formula of a basket of options under random volatility, and to use MontoCarlo to simulate a basket of options to find the numerical solution of the model. Firstly, the classical Black-Scholes option pricing model is studied, based on the hypothesis of this model. The pricing model of multi-asset option and the solution of multi-asset option pricing are studied, and the pricing model and pricing formula of a basket of options are obtained. Secondly, the stochastic volatility model is added to a basket option pricing model, and a basket option pricing formula under random volatility is obtained. Finally, the variance reduction technique of Monto Carlo simulation method is discussed, and the control variable technique is applied to the MontoCarlo simulation of a basket option pricing.
【学位授予单位】：燕山大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.91

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