Levy processes and (quasi-)Monte Carlo methods in finance

金融中的征费流程和（准）蒙特卡罗方法

基本信息

批准号：
299025-2006
负责人：
Lai, Yongzeng
金额：
$ 0.44万
依托单位：
Wilfrid Laurier University
依托单位国家：
加拿大
项目类别：
Discovery Grants Program - Individual
财政年份：
2007
资助国家：
加拿大
起止时间：
2007-01-01 至 2008-12-31
项目状态：
已结题

来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=363662
关键词：
Levy processes quasi Monte Carlo

项目摘要

One of the assumptions in the famous Black-Scholes model used in financial derivative pricing is that the log returns of an asset follow the normal or Gaussian distribution. Although it is widely used in practice, this model has serious drawbacks, such as heavy tail, volatility smile / surface, etc. The stochastic volatility models under the BS framework can improve the results to some extent. A quite different approach is to replace the driving processes for the underlying assets by more realistic ones. Levy processes provide a large variety of distributions to serve such purposes. Empirical studies showed that a special class of Levy process based on the generalized hyperbolic distributions can fit the real financial data much better than the Black-Scholes model. A lot of important work on derivative pricing under the generalized hyperbolic distributions has been done in recent years. However, the use of new distributions results in a lacking of closed formulas and more complex problems that need to be explored. On numerical aspects, efficient numerical methods such as Monte Carlo/quasi-Monte Carlo methods are desperately needed. There are two main objectives of my research. The first one is to construct new quasi-random sequences, also known as the low-discrepancy sequences. The second one is to study problems related to financial derivative pricing and risk management under more realistic models and their numerical computation methods. This research should be of high interest for both academics and industry.

金融衍生品定价中使用的著名黑色 - choles模型中的假设之一是资产的日志返回遵循正常或高斯分布。尽管它在实践中被广泛使用，但该模型具有严重的缺点，例如重型尾巴，波动性的微笑 /表面等。BS框架下的随机波动率模型可以在一定程度上改善结果。一种完全不同的方法是将基础资产的驾驶过程替换为更现实的资产。征税流程提供了各种分布来实现此类目的。经验研究表明，基于广义双曲线分布的特殊征税过程比黑色choles模型更符合实际财务数据。近年来，在广义双曲线分布下的衍生定价上进行了许多重要的工作。但是，新分布的使用导致缺乏封闭公式和需要探索的更复杂的问题。在数值方面，迫切需要有效的数值方法，例如蒙特卡洛/准蒙特卡洛方法。我的研究有两个主要目标。第一个是构建新的准随机序列，也称为低静止序列。第二个是在更现实的模型及其数值计算方法下研究与财务导数定价和风险管理有关的问题。这项研究对于学者和行业都应该引起人们的兴趣。