MATH4210
MATH4210 Financial Mathematics (2010-11)
Lecture Hours and Venues: Every Tuesday 10:30am-12:15pm at LT2, LSB and
Thursday 12:30pm-1:15pm at LT5, LSB
Lecturer Office Hours:
Every Thursday 11:30am-12:15pm, but please send me an email
(rchan@math.cuhk.edu.hk)
or call me first (2609-7970), if possible.
About the Lecturer:
Raymond Chan
About the Tutors:
Tsz Ho LEE (Rm 101, LSB),
Ho Fung LEE (Rm 222C, LSB)
Tutorial Hours and Venues:
Every Monday 12:30pm-1:15pm at G35, LSB and Tuesday 12:30pm-1:15pm at C3, LSB.
Course Objective:
Topics of the course will include: Basic option theory, forward and
futures contracts, model of asset price, Ito's Lemma, asset price
random walk, Black-Scholes model, free boundary problems of options,
discrete random walk model, the binomial methods, Monte Carlo methods,
and if time allows, finite difference method.
Prerequisite:
This course is about the mathematics
of option pricing. Students taking this course are expected
to have good knowledge in probability theory
and partial differential equations.
You can download
Chapter 8 (click here)
of my lecture notes to get a feeling of the
mathematics level required. If it seems difficult
to you, it certainly will be. May be you should then consider
similar courses offered in the University, e.g. FIN4110 or RMS4007.
They most likely will require less mathematical knowledge.
Textbooks:
- Options, Futures and Other Derivatives,
by John Hull (Prentice Hall)
- The Mathematics of Financial Derivatives: a Student Introduction,
by Paul Wilmott, Sam Howison and Jeff Dewynne (Cambridge University Press)
- Mathematical Models of Financial Derivatives,
by Yue-Kuen Kwok (Springer)
References:
- Fundamentals of Futures and Options Market,
by John Hull (Prentice Hall)
- Option Pricing: Mathematical Models and Computations,
by Paul Wilmott, Sam Howison and Jeff Dewynne (Cambridge)
- An Elementary Introduction to Mathematical Finance: Options
and other Topics, by Sheldon Ross (Cambridge)
Lecture Notes:
- The first 7 chapters were modified from the lecture notes prepared by
Prof. Xun Li of The National University of Singapore, and
are based on the book "Options, Futures and Other Derivatives"
by John Hull.
- The remaining chapters are based on the book
"The Mathematics of Financial Derivatives: a Student Introduction" by
Paul Wilmott.
- Some proofs are taken from the book "Mathematical Models of
Financial Derivatives" by Yue-Kuen Kwok.
- Chapter 1 -- Introduction
- Chapter 2 -- Options
- Chapter 3 -- Interest Rates and Forwards
- Chapter 4 -- Put-Call Parity
- Chapter 5 -- Trading Strategies (will not be taught in class)
- Chapter 6 -- Geometric Brownian Motions
- Chapter 7 -- Ito's Lemma
- Chapter 8 -- Black-Scholes Equations
- Chapter 9 -- Numerical Methods for Option Pricing
- Chapter 10 -- Extensions of Black-Scholes Model
Link to the Lecture notes, assignments etc.
Tentative Teaching schedule:
- Week 1: Chapter 1
- Week 2: Chapter 1 (1st Assignment)
- Week 3: Chapter 2
- Week 4: Chapter 2 and Talk by
external speaker (September 30) (2nd Assignment)
- Week 5: Chapter 3
- Week 6: Chapters 4 (3rd Assignment)
- Week 7: Chapters 6
- Week 8: Mid-term (Oct 26) and
Chapter 7
- Week 9: Chapter 7 (4th Assignment)
- Week 10: Chapter 8 (Programming Assignment)
- Week 11: Chapter 8 (5th Assignment)
- Week 12: Chapter 10
- Week 13: Chapters 9.4 and 9.5 (6th Assignment, if time allows)
Talk will be by
Dr. Yves Guo (Executive Director, Equity Derivatives--Goldman Sachs (Asia))
on "Options Derivatives in the Real World"
Assessment Scheme:
- Five/Six Homework Assignments: 15 marks
Solution will be uploaded right after due date.
So no late homeworks will be accepted.
- One Programming Assignment (in any language you like): 5 marks
- One Mid-term (Oct 26, 10:30am-12:00pm): 20 marks
- Final Examination (date centrally scheduled): 60 marks
Important Remarks:
- If you are found cheating, you will automatically get an F
grade in this course and your act will be
reported to the Department for necessary disciplinary actions.
- To avoid copying of programs, your programs may be spot-checked,
i.e. you will be asked questions regarding the statements
in your program when you hand in your program in person.
- Please don't let others copy your assignments or programs as
we don't have a way to tell who is copying who and you may be
liable to the penalties.