金融中的优化与模拟方法  120100MGX017H

学期:2020—2021学年(春)第二学期 | 课程属性:公共选修课 | 任课教师:邓智斌
授课时间: 星期三,第9、10、11 节
授课地点: 教一楼123
授课周次: 2、3、4、5、6、8、9、10、11
授课时间: 星期三,第9、10、11 节
授课地点: 教一楼123
授课周次: 12
授课时间: 星期三,第9、10、11 节
授课地点: 教一楼225
授课周次: 13
授课时间: 星期三,第9、10、11 节
授课地点: 教一楼225
授课周次: 14
课程编号: 120100MGX017H 课时: 30 学分: 1.00
课程属性: 公共选修课 主讲教师:邓智斌 助教:
英文名称: Optimization and Simulation Methods in Finance 召集人:

教学目的、要求

随着金融市场的日益发展,金融工具的多样性和复杂性给决策者既提供了便利也提出了挑战。面对多种选择,如何才能做出最优的决策?面对复杂多变的市场,如何才能合理地规避风险?日益兴起的金融衍生品、证券的定价模型和求解方法又有哪些?
本课程通过理解金融行业中常见的问题,学习金融建模方法,并使用各种数学软件求解实际金融问题。课程的特色在于将优化方法与金融模型的融合,重点阐述了模型求解结果的金融学含义。通过本课程的学习,学生应掌握基本的金融建模方法并能够选用合适的数学工具解决实际问题。

预修课程

线性代数,统计与概率初步,数学建模

教 材

1.	Optimization Methods in Finance, Gerard Cornuejols and Reha Tütüncü, Cambridge University Press, 2007.
2.	Simulation and Optimization in Finance: Modeling with MATLAB @RISK or VBA, Dessislava A. Pachamanova and Frank J. Fabozzi, Wiley Press, 2010.
3.	Financial Models Using Simulation and Optimization I & II, Wayne L. Winston, Palisade Corp., 2008.
4.	Numerical Methods and Optimization in Finance, Manfred Gilli, Dietmar Maringer and Enrico Schumann, Academic Press, 2011. 
5.	Financial Modeling, 3rd edt. Simon Benninga, MIT Press, 2008.

主要内容

Part I: Optimization in Finance
Lecture 1: Introduction to Financial Optimization
Introduction to the course; Optimization problems and modeling; Sample examples; Mathematical preliminary
Lecture 2: Linear Optimization and MATLAB
CVX solver for MATLAB; Introduction to CVX; Example: Cash Flow Matching problem
Lecture 3: Dual theory of LP and Sensitivity Analysis
Duality theorems in LP; Sensitivity analysis and shadow price; Example: Cash Flow Matching problem
Lecture 4: LP for Asset Pricing and Arbitrage
Replication; Risk-neutral probabilities; Fundamental theorem of asset pricing; Example: Arbitrage detecting using LP
Lecture 5: Quadratic Optimization
Quadratic programming problem; Optimality conditions, Interior-point methods, Software for QP
Lecture 6: QP and Portfolio Optimization
Mean-variance model; Efficient frontier;Capital Market Line; VaR & CVaR
Lecture 7: Integer Programming
IP model for constructing index fund; LP model for constructing index fund; Example: index fund for S&P 500; Revisit portfolio optimization
Part II: Simulation in Finance
Lecture 8: Simulation in MATLAB
Introduction to Monte Carlo simulation; Variance reduction technique; Quasi-random number; Simulation methods in MATLAB
Lecture 9: Models for Asset Price Dynamics
Binomial trees; Arithmetic random walks; Geometric random walks; mean reversion; 
Lecture 10: Pricing Derivatives by Simulation
Option prices by simulation; Asian and barrier options prices by simulation; Pricing for options and interest rate derivatives; 
Lecture 11: Pricing RMBS by Simulation
Types of RMBS structures; Prepayment models; Interest rate models; Simulation for pricing RMBS; Sensitivity analysis by simulation

参考文献

1.	Optimization Methods in Finance, Gerard Cornuejols and Reha Tütüncü, Cambridge University Press, 2007.
2.	Simulation and Optimization in Finance: Modeling with MATLAB @RISK or VBA, Dessislava A. Pachamanova and Frank J. Fabozzi, Wiley Press, 2010.
3.	Financial Models Using Simulation and Optimization I & II, Wayne L. Winston, Palisade Corp., 2008.
4.	Numerical Methods and Optimization in Finance, Manfred Gilli, Dietmar Maringer and Enrico Schumann, Academic Press, 2011. 
5.	Financial Modeling, 3rd edt. Simon Benninga, MIT Press, 2008.