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Department of Applied Mathematics

 

Stochastic Calculus for Finance

Prerequisites: Probability Theory
Content: Stochastic Calculus for Finance is an important course that the stochastic analysis is applied into mathematical finance. It mainly solves the pricing of financial assets with stochastic analysis theory. The contents will include the basic theory of measure such as the filtration, the probability space and measure, the simple stochastic process such as Markov process, random walk, Brownian motion and the discrete models of asset pricing. Through teaching, the students can master the methods and the idea of solving the financial problem with stochastic analysis, which can lay a solid foundation for the students’ future learning of continuous time model and its application in finance.
 
Pricing of Financial Derivatives
Prerequisites: Mathematical Analysis, Linear Algebra, Probability Theory, Mathematical Statistics, Stochastic Calculus for Finance
Content: The pricing theory of financial derivatives is the main course of financial mathematics. This course mainly introduces the no arbitrage theory, Brownian motion, the binomial tree model of option pricing, the pricing of European option and American option and so on. Through learning the course, the students can master the basic principle and method of the financial derivatives’ pricing, and can use the relevant software for numerical simulation.
 
Fixed Income Securities
Prerequisites: Finance, Probability Theory, Statistics Analysis, Stochastic Calculus for Finance
Content: The course will introduce the price conventions of fixed income securities, zero-coupon bond, coupon bond, convexity, interest rate term structure, bond with embedded option, interest rate futures, options and swaps. Though learning, the students can master the basic knowledge and the basic pricing theory of fixed income securities.
 
Financial Time Series Analysis  
Prerequisites: Mathematical Statistics, Econometrics for Finance, Finance
Content: Financial Time series model is an important part of the practical financial models and is the application of time series analysis in various financial fields such as stock market, bond market, financial derivative instrument market and foreign exchange market. This course mainly introduces financial econometrics model and its application in the modeling of financial time series data. Main content includes: risk value calculation, high frequency data analysis, stochastic volatility modeling, markov chain and monte carlo method. Powerful econometric analysis software Eviews would be taught in this course.
 
Computational Methods in Finance
Prerequisites: Mathematical Analysis, Linear Algebra, Finance
Content: With the rapid development and extensive application of computers, people are increasingly realizing that scientific calculation is an important method of scientific research in a large number of areas of finance. Students majored in financial mathematics should be provided with the knowledge and capacity in this aspect. The main content of this course includes Matlab Software, extraction of root from an equation, numerical solution of a system of linear equations, interpolation method, the method of fitting curve, numerical integration and differentiation, Monte-Carlo methods, numerical solution of the differential equation, one-dimensional search method of extreme value problem and applications in finance, etc.
 
Portfolio Management
Prerequisites: Mathematical Analysis, Linear Algebra, Probability Theory, Mathematical Statistics
Content: Portfolio Management introduces the line of capital market, CAPM, the extended CAPM, the estimation of beta coefficient and arbitrage pricing, the main contents of modern portfolio theory, utility function, risk aversion, stochastic dominance, the efficient frontier of portfolio model and the mean-variance model. Through learning the course, students can master the basic theory of portfolio management and apply the learned theory, such as the Markowitz’s mean-variance model and sharp single factor model, into the actual portfolio and asset allocation by the relevant software.
 
Optimization Methods in Finance
Prerequisites: Mathematical Analysis, Linear Algebra, Probability Theory, Mathematical Statistics, Finance
Content: Optimization is one of the most important tools in finance, which is applied to simulation, computation of securities’ pricing, estimation of risks and selection of hedging strategies. This course will cover such methods as Linear Programming, Nonlinear Programming, Integer Programming, Dynamic Programming and other methods. Students can use them to solve typical optimization problems arising in finance such as asset-liability management, option pricing and hedging, risk management and portfolio optimization.