Course Coordinator: Dr Tony M T Chan, Grad Dip, MPhil (CUHK); PhD (CityU)
Course Developer: The Open University, UK, Course Team
MATH S390 Quantitative Models for Financial Risk is a 5-credit, one-semester, higher-level course. MATH S390 is about the use of mathematics to solve real-life applications. You will learn how to represent real world financial problems through various types of mathematical methods (e.g. Black–Scholes models).
This course is presented at 12-month intervals.
Advisory prerequisite(s)
Students are advised to have studied a basic statistics course such as MATH S248 / MATH S280 and a mathematics course such as MATH S207 / MATH S221, or to have achieved an equivalent level before studying this course.
This course aims to:
- provide students with a basic understanding of various option pricing formulae, hedging techniques, bond models and interest rates.
- introduce different types of financial risks and the common quantitative methods used to set up financial derivative models, and to analyze and interpret various problems and risks arising in financial engineering.
- introduce basic statistical and mathematical theory, in particular the stochastic and continuous-time differentiation models required for computing the pricing of financial options and other derivative securities for the assessment of risk.
- enhance students' ability to elaborate on the assumptions for developing options models, and to equip students with the ideas of forwards and options and the concept of non-arbitrage in order to consider the pricing of financial derivatives.
- use the binomial model and the Black-Scholes option pricing model to interpret the valuation of European and American options.
- develop students' professional skills in stochastic calculus and its applications for risk analysis and finance.
- teach students the properties of Brownian motion and how to apply them to evaluate the price of stock options problems.
- develop quantitative financial risk models through the multi-variable calculus and differential equations.
Contents
The course covers the following topics:
Unit 1 Introduction to financial risk and quantitative process
- Basic terminologies used in the financial industry
- Various financial instrument and their risks
- Application of the game theory method to explain the idea of arbitrage
Unit 2 Tree models for stocks and options
- The principle of no-arbitrage opportunity in evaluation of financial instrument, and application to price linear derivative securities
- Calculating the payoff, and interpreting the profit of basic derivatives contracts, such as forward contracts, futures contracts, American and European put and call options, simple commodity swaps, and interest rate swaps
Unit 3 Mathematical methods for the Black–Scholes model
- Application of the stochastic calculus to model Brownian motion, and using Ito's Lemma to derive the stochastic differential equations
- Application of the no-arbitrage principle and risk-neutral (martingale) pricing
- Deriving a Black–Scholes differential equation for pricing option
- Adopting an appropriate method to solve the Black–Scholes differential equation analytically
- Interpreting the overall investment return based on the computational results
Unit 4 Risk models in hedging
- Constructing a hedging strategy for a variety of risks
- Identifying cash flows in swap transactions
- Evaluating alternative hedge positions
Unit 5 Quantitative methods for bond models and interest rate options
- More sophisticated risk models used by the financial analyst/planner to manage stocks, bonds and mixed portfolios
- Calculations of yields, continuous compounding, and par, forward and zero yield curves
Unit 6 Financial risk models in practice
- Modelling the payoff structures of CBBCs & Accumulator contracts
- Discussion of volatility smile, volatility matrices and the volatility term structure
- Evaluating the implied volatility under the Black-Scholes model framework
- Calculating the Value at Risk for single-asset and multi-asset cases
Learning support
There will be six two-hour tutorials and three surgeries throughout the course.
Assessment
There are three assignments (best two out of three will be counted) and a final examination. Students are required to submit assignments via the Online Learning Environment (OLE).
Online requirement
This course is supported by the Online Learning Environment (OLE). You can find the latest course information from the OLE. Through the OLE, you can communicate electronically with your tutor and the Course Coordinator as well as other students. To access the OLE, students will need to have access to the Internet. The use of the OLE is required for the study of this course and you can use it to submit assignments.
Equipment
Students will need access to a computer with an Internet connection and spreadsheet software, e.g. Excel. A scientific calculator is also necessary.
Set book(s)
There are no set books for this course.
Student with disabilities or special educational needs
The visual components of this course may cause difficulties for students with visual impairment. You are encouraged to seek the advice from the Course Coordinator before enrolling on the course.
