Some Problems on Derivative Pricing and Portfolio Optimization under More Realistic Asset Price Models

更现实的资产价格模型下衍生品定价和投资组合优化的一些问题

• 批准号: RGPIN-2014-03574
• 负责人: Lai, Yongzeng
• 金额: $ 0.8万
• 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: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=565952
• 关键词: Some; Problems; Derivative; Pricing; Portfolio

Derivative pricing, hedging, portfolio optimization and risk management are important problems in modern finance. The Black-Scholes-Merton's model is well known for option pricing. However, empirical studies using worldwide real financial data show that models based on some special Levy processes, called subordinated Brownian motions or time-changed Brownian motions, are more accurate than the Black Scholes-Merton's model. There are many new and challenging problems, both theoretical and computational, under the more realistic and more complex Levy process models. Efficient numerical methods dealing with these problems under Levy models are in high demand since lack of closed formulas under Levy models. The Monte Carlo (MC)/quasi-Monte Carlo (QMC) simulation methods have become indispensable tools in financial engineering in handling high dimensional situations. This research program will apply advanced mathematical tools, such as stochastic analysis, stochastic optimal control, (stochastic) differential equations, Malliavin calculus, etc., and efficient numerical methods to solve certain problems in portfolio optimization, financial derivative pricing, hedging and risk management under the more realistic Levy process models. The problems I plan to tackle include the following: 1. Derivation of optimal portfolios and efficient frontiers for portfolio optimization problems. 2. Construction of efficient Monte Carlo and quasi-Monte Carlo methods with applications to options pricing, portfolio optimization, etc. 3. Simulation of multi-asset derivatives by efficient Monte Carlo and quasi-Monte Carlo methods. 4. Derivation of formulas for Multi-asset option Greeks and simulation of these Greeks. 5. Pricing and hedging American style options. The above problems are new and important both for academic research and financial industrial applications, and the results can be beneficial to the Canadian financial relevant industries.

衍生品定价，对冲，投资组合优化和风险管理是现代金融中的重要问题。黑色 - choles-Merton的模型以期权定价而闻名。但是，使用全球实际财务数据的实证研究表明，基于某些特殊征税过程的模型（称为次级布朗尼动议或随时间变化的布朗尼动议）比Black Scholes-Merton的模型更准确。在更现实，更复杂的征费过程模型下，理论和计算都有许多新的和具有挑战性的问题。在征税模型下处理这些问题的有效数值方法的需求很高，因为征税模型缺乏封闭公式。 Monte Carlo（MC）/Quasi-Monte Carlo（QMC）仿真方法已成为处理高维情况的金融工程中必不可少的工具。该研究计划将采用高级数学工具，例如随机分析，随机最佳控制，（随机）微分方程，Malliavin Colculus等，以及有效的数值方法，以在更现实的征费过程模型下解决投资组合优化，金融衍生品定价，套期保值和风险管理方面的某些问题。我打算解决的问题包括以下内容：1。最佳投资组合和有效边界的推导，用于投资组合优化问题。 2。构建有效的蒙特卡洛和准蒙特卡洛方法，其应用于期权定价，投资组合优化等。3。通过有效的蒙特卡洛和Quasi-Monte Carlo方法模拟多资产衍生物。 4。用于多资产选项的公式的衍生和这些希腊人的模拟。 5。定价和对冲美国风格的选择。以上问题对于学术研究和金融工业应用都是新的，并且结果可能对加拿大金融相关行业有益。