Teaching

This module is designed to provide students with the basic concepts and theories involved in statistical methods. Major topics include organisation and presentation of data in an informative way, some useful probability distributions used in statistical inference, estimation of parameters and hypothesis testing.

This course starts with presenting standard topics in simulation including random variable generations, variance reduction methods and statistical analysis of simulation outputs. The course then reviews the applications of these methods to derivative security pricing. Topics addressed include importance sampling, martingale control variables, stratification and the estimation of derivatives. Additional topics include the use of low discrepancy sequence (quasi-random numbers), pricing American options and scenario simulation for risk management.

This course aims at understanding the application of derivatives theories for the practical risk management. It starts by reviewing basic concepts of pricing and hedging derivatives, like risk-neutral valuation, arbitrage strategies, hedging strategies, implied volatilities and the Greeks. The Value-at-Risk framework for derivatives positions is discussed. Student will also learn how to apply option theoretic approach to credit risk management.

This course aims at providing a focused introduction to various concepts of risk and risk measures from a scientific perspective. The course will discuss the various roles that risk plays in insurance and financial applications. Current risk measures such as value at risk and shortfall risk will be introduced. These measures will be calculated for recent financial losses to illustrate their usefulness in risk management.

Fixed income securities are highly sensitive to the fluctuation of interest rates. Thus interest rate modeling becomes crucial for pricing and managing fixed income securities. This course introduces various types of fixed income securities and interest rate models. It covers the celebrated Heath-Jarrow-Morton (HJM) model as well as some term-structure models including Ho-Lee, Hull-White and the CIR models.