Bates模型下障碍期权定价研究

发布时间：2018-04-27 06:16

本文选题：Bates模型 + 障碍期权　；参考：《广西师范大学》2013年硕士论文

【摘要】：自20世纪60年代末,市场上出现障碍期权交易,障碍期权便发展迅速,口前,障碍期权的种类已超过数十种,障碍期权的出现给风险管理者们提供了更有效的方法,让他们不必为他们认为不可能到达的价格支付费用。障碍期权的定价也自Fisher Black、Myron Scholes和Robert Merton在期权定价领域取得了重大突破之后,障碍期权在金融市场得到迅猛发展。其相对于标准的欧式、美式期权,交易方式灵活、收益更符合投资者意愿、而且价格更加便宜,因此也更受投资者的喜爱。所以如何给这类奇异期权定价已成为金融数学领域研究的热点课题之一。虽然经典的Black-Sholes模型简明、易于计算,但其过于理想化的假设,使经典的Black-Sholes模型在描述系统风险方面与观测数据不符,因此人们不断尝试削弱Black-Sholes模型的假设条件,使之能更好的拟合金融数据,大量实证研究表明：跳扩散模型、随机波动率模型在刻画股价行为方面比经典的Black-Sholes模型更符合实际,因此成为目前研究的前沿热点课题,但在国内外对Bates模型下障碍期权定价的研究成果并不多见。障碍期权(Barrier Options)的终期收益不仅依赖于标的资产到期日的价格,而且还依赖于标的资产在整个合约有效期内是否达到规定的障碍水平.由于它具有这种灵活的条款,因此其价格比标准期权便宜,并深受投资者的喜爱.本文将在Bates模型下,研究欧式、美式障碍期权定价。主要工作包括：第一章介绍了期权定价以及本文的研究意义,国内外对Bates模型下障碍期权定价的研究现状,以及本文的选题依据. 第二章在股票价格满足Bates模型下讨论离散时间情形的欧式障碍期权定价,应用半鞅Ito公式、多维随机变量的特征函数、Girsanov测度变换以及Fourier反变换等随机分析方法,给出离散时间情形的欧式障碍期权价格的显示解,并利用数值计算分析了障碍期权价格受波动率参数的影响. 第三章在第二章Bates市场模型下讨论美式期权及美式障碍期权定价,首先研究美式期权定价,先用3点G-J法对百慕大期权进行分析,在得出美式期权定价,其思想来自Geske和Johnson的分析.在用2点G-J法对百慕大障碍期权进行离散化处理对其进行定价,进而对美式障碍期权进行定价,最后进行了数值计算且对结果进行了分析. 第四章总结本文的主要工作和有待进一步研究的问题.
[Abstract]:Since the late 1960s, barrier options have developed rapidly in the market, and the types of barrier options have exceeded dozens. The emergence of barrier options has provided more effective methods for risk managers. So they don't have to pay for prices they don't think they can reach. The pricing of barrier options has also developed rapidly in the financial market since the breakthrough in the field of option pricing made by Fisher Black-Myron Scholes and Robert Merton. Compared to standard European and American options, they are more flexible, more profitable and cheaper, and therefore more popular with investors. So how to price this kind of strange option has become one of the hot topics in the field of financial mathematics. Although the classical Black-Sholes model is simple and easy to calculate, it is too idealized to make the classical Black-Sholes model inconsistent with the observed data in describing the system risk. Therefore, people are constantly trying to weaken the hypothetical conditions of the Black-Sholes model. A large number of empirical studies show that the jump diffusion model and the stochastic volatility model are more practical than the classical Black-Sholes model in describing the behavior of stock price. However, there are few researches on barrier option pricing under Bates model at home and abroad. Barrier options (Barrier options) depends not only on the maturity price of the underlying asset, but also on whether the underlying asset reaches the specified barrier level during the whole term of the contract. Because of its flexible terms, it is cheaper than standard options and popular with investors. This paper will study the pricing of European and American barrier options under Bates model. The main tasks include: The first chapter introduces the option pricing and the significance of this paper, the domestic and foreign research status of barrier option pricing under the Bates model, as well as the basis of this paper. In chapter 2, we discuss the pricing of European barrier options with discrete time under the Bates model of stock prices. We apply the semi-martingale Ito formula, the eigenfunction of multidimensional random variables, the Girsanov measure transformation, and the Fourier inverse transformation. The explicit solution of the price of European barrier options in discrete time is given, and the influence of volatility parameters on the price of barrier options is analyzed by numerical calculation. The third chapter discusses the pricing of American options and American barrier options under the second chapter of Bates market model. Firstly, the pricing of American options is studied, and the Bermuda option is analyzed with the three-point G-J method, and the pricing of American options is obtained. Its thought comes from the analysis of Geske and Johnson. In this paper, a 2-point G-J method is used to discretize Bermuda barrier options to price them, and then American barrier options are priced. Finally, numerical calculations are carried out and the results are analyzed. The fourth chapter summarizes the main work of this paper and the problems to be further studied.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F224;O211.6

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