M.Phil.-Ph.D. Programme : Area IV: Financial Engineering

 

SEEM 5340 Stochastic Calculus
SEEM 5360 Term Structure Modeling of Interest Rates
SEEM 5370 Topics in Behavioral Finance and Economics
SEEM 5410 Optimal Control
SEEM 5570 Numerical Methods in Finance 
SEEM 5620 Data Warehousing for Financial Engineering 
SEEM 5670 Advanced Models in Financial Engineering


 

SEEM 5340 Stochastic Calculus

Introduction to continuous time stochastic processes. Brownian motions: explicit constructions, properties, quadratic variation, the Cameron-Martin-Girsanov formula, multidimensional Brownian motions. Stochastic Integration: definition, Ito’s formula, martingale representation, time change, Girsanov’s Theorem, local time and Tanaka’s formula. Stochastic differential equations and diffusion processes: strong and weak solutions, diffusions, the Feynman-Kac formula, backward stochastic differential equations. Levy processes: definition, the Levy-Khinchin representation, the Levy-Ito decomposition, the Esscher transform.

 

SEEM5360 Term Structure Modeling of Interest Rates

The course is a systematic introduction to the development, analysis and implementation of interest rate models for pricing and hedging of fixed income derivatives. The materials will span the following aspects: linear interest rate product and yield curve construction; vanilla interest rate options and single rate models; interest rate exotics and the modeling of rates term structure. If time permits, we will also discuss typical trading strategies in the fixed income space, as well as hedging and management of interest rate exposures for fixed income portfolios, cash or derivative.

SEEM5370 Topics in Behavioral Finance and Economics

Behavioral finance/economics is a relatively new field, which assumes economic agents to be irrational, in contrast to the rational assumption in neoclassical finance/economics. In this course, I introduce the history of behavioral finance and economics, and the recent development and potential research topics in this field. I will first introduce the foundation of neoclassical finance, portfolio selection and asset pricing models in neoclassical finance, and empirical evidence that is inconsistent with models in neoclassical finance. Then, I will introduce the basic principles of behavioral finance/economics, portfolio selection and asset pricing problems in neoclassical finance and new approaches to these problems, and empirical studies that are consistent with models in behavioral finance/economics. In addition to the recent development in behavioral finance/economics, I will also propose a variety of open research problems in this field.
 

SEEM 5570 Numerical Methods in Finance

This course emphasizes the use of numerical methods for solving financial problems. The numerical methods include: binomial trees, Monte Carlo simulation, stochastic programming, linear/quadratic control models and semidefinite programming techniques. Those techniques will be applied, among other things, to: option pricing, index tracking, portfolio optimization, interest rate models, and asset/liability management.

 

SEEM5410 Optimal Control

Dynamic continuous-time systems. Examples, modelling, and classification of optimal control problems. Pontryagin's maximum principle: adjoint equation, Hamiltonian system, and sufficient condition of optimality. Bellman's dynamic programming: principle of optimality, Hamilton-Jacobi-Bellman equation, and verification theorem. Linear quadratic control: Riccati equation and linear matrix inequality. Introduction to numerical methods of solving optimal control problems.

 

SEEM 5620 Data Warehousing for Financial Engineering

This course addresses the data and decision aspects of financial information systems. The data aspect includes collection, cleansing, storage, and retrieval of quantitative and qualitative financial data. The decision aspect include on-line analytical processing on financial data and data mining for nontrivial data pattern and knowledge.

SEEM 5670 Advanced Models in Financial Engineering

This course covers various applications of engineering technicalities in financial modelling. Emphasis will be on two main topics: investment portfolio optimization and financial derivative pricing. We introduce dynamic programming approach, martingale and PDE numerical solutions, Monte Carlo simulation methods for solving these two problems.