不完备市场中的几类期权定价研究

发布时间：2018-04-09 06:39

本文选题：Bayes法则　切入点：测度变换　出处：《华东师范大学》2012年博士论文

【摘要】：近年来,随着金融衍生产品市场的发展,衍生产品的定价,风险管理等问题变得越来越重要.为了描述不断变化的经济环境,更多复杂的模型被提出.我们根据风险中性定价理论研究在市场不完备的情况下几类期权的定价问题.具体内容如下： 1.第一章首先介绍了期权的概念及资产定价的发展,接着,介绍了不完备市场中的期权定价,然后简要说明了信用风险模型的分类和研究状况,最后,给出了一些基本定义和定理及本论文的主要工作. 2.第二章考虑了幂函数型期权的定价问题.为了反映市场中风险资产的价格变化过程,我们首先假设风险资产的价格过程服从跳扩散模型,其次假定市场中参数随连续时间的马尔科夫链状态的转移而变化.在第一种情况下,我们假定市场利率服从Vasicek模型并且假定风险资产与市场利率是相关的,通过给定一个等价鞅测度我们得到了幂函数型期权的价格公式.在第二种情况下,我们假定市场利率,风险资产的期望收益率和波动率都与市场经济状态有关,市场经济状态由一连续时间马尔科夫链来描述.由于市场是不完备的,利用regime switching Esscher变换得到了一个等价鞅测度,给出了当标的资产价格服从马尔科夫调制的几何布朗运动时的幂函数型期权价格公式. 3.第三章讨论了约化模型下具有信用风险的几类期权的定价问题.由于不可预见的事件的发生可能会导致违约强度发生剧烈的变化,我们假设违约强度服从一个跳扩散模型.此外,我们假定期权卖方可能发生违约并且回收率是一个常数.在约化模型下,分别给出了具有信用风险的欧式期权,幂函数型期权以及交换期权的价格公式. 4.第四章研究了具有随机死亡强度的担保年金期权(Guaranteed Annuity Options)的定价问题.为了符合实际情况,我们在死亡强度中增加了“跳”的因素.我们假设死亡强度服从跳扩散模型,标的资产价格过程服从随机波动率模型,利率满足Vasicek模型,并且假设这些过程都是相关的,给出了担保年金期权的价格公式. 5.第五章在局部风险最小的标准下考虑套期保值策略以及最小鞅测度.当标的资产价格服从跳扩散模型或者马尔科夫调制的体制转换模型时,市场是不完备的,这也意味着市场中的未定权益不能通过自融资策略来套期保值.我们分别给出了跳扩散模型下内幕交易者的局部风险最小套期保值策略以及具有随机波动率的马尔科夫调制跳扩散过程下的相应策略. 综上所述,本文研究了标的资产服从不同模型时的几类期权的定价问题.获得了跳扩散模型和regime switching模型下的幂函数型期权以及随机死亡强度下的担保年金期权的价格公式.在约化模型下考虑了具有信用风险的几类期权的定价.此外,在市场不完备的情况下,考虑套期保值问题,给出了局部风险最小套期保值策略和最小鞅测度。
[Abstract]:In recent years, with the development of financial derivatives market, the pricing and risk management of derivatives become more and more important.In order to describe the changing economic environment, more complex models have been proposed.According to the risk neutral pricing theory, we study the pricing problems of several kinds of options under the condition of incomplete market.The details are as follows:1.The first chapter introduces the concept of option and the development of asset pricing, then introduces the option pricing in incomplete market, then briefly describes the classification and research status of credit risk model.Some basic definitions and theorems are given as well as the main work of this paper.2.In the second chapter, we consider the pricing of power function options.In order to reflect the price change process of risk assets in the market, we first assume that the price process of risk assets is based on the jump diffusion model, and then assume that the parameters in the market change with the transition of Markov chain state in continuous time.In the first case, we assume that the market interest rate is dependent on the Vasicek model and that the risk asset is related to the market interest rate. By giving an equivalent martingale measure, we obtain the price formula of the power function option.In the second case, we assume that the market interest rate, the expected return rate of risk assets and volatility are all related to the market economy state, which is described by a continuous Markov chain.Because the market is incomplete, an equivalent martingale measure is obtained by using regime switching Esscher transform, and the power function option price formula is given when the underlying asset price is in geometric Brownian motion modulated from Markov.3.In chapter 3, we discuss the pricing of several kinds of options with credit risk under reduced model.Since unexpected events may lead to drastic changes in default intensity, we assume that the default strength service is diffused from a jump model.In addition, we assume that the option seller may default and the recovery rate is a constant.Under the reduced model, the price formulas of European option, power function option and exchange option with credit risk are given respectively.4.In chapter 4, we study the pricing of guaranteed Annuity options with random death intensity.To fit the situation, we added a jump factor to the death intensity.We assume that the death intensity clothing jump diffusion model, the underlying asset price process from the stochastic volatility model, the interest rate satisfy the Vasicek model, and assume that these processes are all relevant, and give the guaranteed annuity option pricing formula.5.Chapter 5 considers hedging strategy and minimum martingale measure under the criterion of minimum local risk.When the underlying asset price is from the jump diffusion model or the Markov modulation system transformation model, the market is incomplete, which also means that the contingent equity in the market can not be hedged by self-financing strategy.We give the local risk minimization strategy for insider traders under jump diffusion model and the corresponding strategies for Markov modulation jump diffusion process with random volatility.To sum up, this paper studies the pricing of several kinds of options under different models of underlying assets.The price formulas of guaranteed annuity options under jump diffusion model and regime switching model and guaranteed annuity options with random death intensity are obtained.The pricing of several kinds of options with credit risk is considered in the reductive model.In addition, when the market is not complete, the local risk minimum hedging strategy and the minimum martingale measure are given.
【学位授予单位】：华东师范大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：F224;F830.9

【共引文献】