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: Mr. Tsz-Ho Lee and Guojian Yin (Email: thlee, gjyin@math.cuhk.edu.hk, Office: Rm 101, LSB).

Tutorial Hours and Venues: Every Thursday 11:30am-12:15pm at LT5, LSB and Thursday 1:30pm-2:15pm at LT5, 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)

• 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:

1. 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.
   
2. The remaining chapters are based on the book "The Mathematics of Financial Derivatives: a Student Introduction" by Paul Wilmott.
3. 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

Tentative Teaching schedule:

• Week 1: Chapter 1
• Week 2: Mid-Autumn Festival and Chapter 1 (1st Assignment)
• Week 3: Chapter 2
• Week 4: Chapter 2, Typhoon--class cancelled (2nd Assignment)
• Week 5: Chapter 3
• Week 6: Chapter 4 (3rd Assignment) and Quiz 1 (Oct 13)
• Week 7: Chapters 4,6
• Week 8: Chapters 6,7 (4th Assignment)
• Week 9: Chapter 7
• Week 10: Chapter 8 (5th Assignment) and Quiz 2 (Nov 10)
• Week 11: Chapter 8 (Programming Assignment)
• Week 12: No class on Nov 22 and talk by Dr. Guo (Nov 24)
• Week 13: Chapter 9.4 and 9.5 (6th Assignment)
• Supplementary class (December 6 (Tuesday), 10:30am-12:15pm at LT5, LSB): Chapter 10

Talk on November 24 will be by Dr. Yves Guo (Executive Director, Head of Financial Engineering for Equities at Morgan Stanley (Asia Pacific))
on "Option 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
  
• Two quizzes (Oct 13 and Nov 10, from 12:30pm to 1:15pm): 20 marks
  
• Final Examination (date centrally scheduled): 60 marks
  Cover Chapters 1 to 9.6 and Section 10.5