Levy过程多维化方法在期权市场应用的比较研究

发布时间：2018-09-05 15:28

【摘要】：金融资产的多维模型在现代金融市场中的应用越来越重要,如多资产衍生品定价、投资组合的风险管理和最优投资组合选择等领域。期权作为一种衍生证券,它的价格变化规律受标的资产价格变化的影响。由于标的资产价格存在不连续性,B-S模型不能精准地刻画期权价格,所以将带跳跃的Levy过程引入期权市场。随着期权创新的迅速发展和奇异期权的日益增多,期权的结构越发复杂,对其定价的难度也越来越高。尤其是标的资产为多个资产的期权,即多资产期权。因此,需要研究Levy过程的多维化方法。本文针对期权定价B-S模型存在的缺陷,以及多资产期权或高维资产期权定价的维数灾难问题,讨论了期权定价计算的复杂性和其它数值方法及其优缺点,并且特别对蒙特卡罗模拟方法进行重点研究。一篮子期权和彩虹期权都是多资产奇异期权的典型代表。本文运用多维带跳的Levy过程中的多维Variance Gamma模型对篮子期权和彩虹期权中的择次好彩虹期权进行定价。具体过程为使用随机时钟变化技术,通过一个共同的r(Gamma)从属过程时变几何布朗运动建立多维Variance Gamma模型。并运用蒙特卡罗模拟方法进行实证分析,与多维B-S模型进行比较,得出多维Variance Gamma模型的结果优于多维B-S模型,更加符合现实的期权市场。
[Abstract]:Multi-dimensional models of financial assets are becoming more and more important in modern financial markets, such as multi-asset derivatives pricing, portfolio risk management and optimal portfolio selection. As a kind of derivative securities, option is influenced by the change of underlying asset price. Because there is discontinuity in the underlying asset price, the B-S model can not accurately describe the option price, so the Levy process with jump is introduced into the option market. With the rapid development of option innovation and the increasing number of exotic options, the structure of options becomes more and more complex, and the pricing of options becomes more and more difficult. In particular, the underlying asset is multiple assets options, that is, multiple assets options. Therefore, it is necessary to study the multidimensional method of Levy process. In this paper, the complexity of option pricing calculation, other numerical methods and their advantages and disadvantages are discussed, aiming at the defects of B-S model of option pricing and the dimensionality disaster of multi-asset option or high-dimensional asset option pricing. The Monte Carlo simulation method is especially studied. A basket of options and rainbow options are typical representatives of multi-asset exotic options. In this paper, we use the multidimensional Variance Gamma model in the multi-dimensional Levy process to price the second-best rainbow options in basket options and rainbow options. The multi-dimensional Variance Gamma model is established by using a common r (Gamma) dependent process with time-varying geometric Brownian motion using the random clock variation technique. Compared with the multi-dimensional B-S model, the result of the multidimensional Variance Gamma model is better than that of the multi-dimensional B-S model, which is more in line with the reality of the option market.
【学位授予单位】：天津科技大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F224;F830.9

【相似文献】