基于Ornstein-Uhlehbeck过程的亚式期权定价

发布时间：2018-07-23 12:19

【摘要】：近年来，亚式期权成为金融衍生市场的新热点．亚式期权与标准期权相比，期权费和对冲成本更低．另外，亚式期权是根据平均值定价的，可以减少标的资产被人为操控的机会．基于这两个优点，它受到一些公司的青睐．因此亚式期权定价的研究符合市场需要，具有实际意义．本文用精算定价的方法对股价遵循广义指数Ornstein-Uhlenbeck过程，利率满足Hull-White模型的亚式期权定价进行了研究，全文共六章．第一章介绍期权的基本知识，包括期权、期权市场和期权定价理论的产生和发展，介绍了本文的主要工作．第二章介绍了股票模型、伊藤引理、Black-Sholes模型及三种常用的期权的数值计算方法．用Hurst指数对股票进行了MATLAB数值分析，设计了一个Hurst指数择时策略，通过实例说明该策略取得了非常理想的效果，并推知Hurst指数择时策略适合长期投资者．第三章介绍了亚式期权定价的研究现状、定价方法和几个经典的定价公式．第四章介绍了基础的Ornstein-Uhlenbeck过程和广义指数Ornstein-Uhlenbeck过程，通过这些模型的比较，广义指数Ornstein-Uhlenbeck过程具有明显的回归性：如果股票价格发生了偏离，该模型令其有回归的趋势．正是因为这一优越性，本文选用这一模型来描述股票过程．第五章用精算定价的方法对股价遵循广义指数Ornstein-Uhlenbeck过程，利率满足Hull-White模型的亚式期权定价进行了研究．说明了选用精算定价方法的原因：它缓解了Black-Sholes期权定价过高和统计定价过低的矛盾，具有一定优势．最后，在不考虑红利支付的情况下，得到了算术平均亚式期权的看涨和看跌期权定价公式，几何平均亚式期权的看涨和看跌期权定价公式．第六章总结了论文的工作并提出展望．
[Abstract]:In recent years, Asian options have become a new hot spot in the financial derivatives market. Asian options have lower option fees and hedging costs than standard options. In addition, Asian options are priced on average. It can reduce the chance of the underlying asset being manipulated artificially. Based on these two advantages, it is favored by some companies. Therefore, the study of Asian option pricing meets the needs of the market. This paper uses the actuarial pricing method to study the Asian option pricing which follows the generalized exponential Ornstein-Uhlenbeck process and the interest rate satisfies the Hull-White model. The first chapter introduces the basic knowledge of options, including the emergence and development of options, option market and option pricing theory, and introduces the main work of this paper. The Black-Sholes model of Ito Lemma and the numerical calculation methods of three kinds of commonly used options are used. The MATLAB numerical analysis of stock is carried out with Hurst exponent, and a Hurst exponent timing strategy is designed. An example is given to show that the strategy has a very good effect. And the Hurst index timing strategy is suitable for long-term investors. Chapter three introduces the current situation of Asian option pricing. Chapter 4 introduces the basic Ornstein-Uhlenbeck process and the generalized exponential Ornstein-Uhlenbeck process. The generalized exponential Ornstein-Uhlenbeck process has obvious regression: if the stock price deviates, the model has a regression trend. This paper uses this model to describe the stock process. Chapter 5 uses the actuarial pricing method to follow the generalized exponential Ornstein-Uhlenbeck process for the stock price. The paper studies the pricing of Asian option with Hull-White model, and explains the reason of choosing actuarial pricing method: it alleviates the contradiction between excessive pricing of Black-Sholes option and too low statistical pricing. Finally, it has some advantages. Without taking into account the dividend payment, the pricing formulas of call and put options for arithmetic average Asian options are obtained. The pricing formulas of the geometric average Asian option are put and call options. Chapter 6 summarizes the work of this paper and puts forward the prospect.
【学位授予单位】：哈尔滨工程大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

【参考文献】