## MATH4210 Financial Mathematics, 2012-13

### Announcement

• The first tutorial will start from 23-1-2013
• The first assignment is uploaded
• The second assignment is uploaded
• Lectures of Part I is over at 30-01-2013
• The course note (below) is only some parts of the classroom lectures -- it is for your convenience. You are responsible for ALL contents of the classroom lectures !
• Lectures of Part II is over at 25-02-2013
• The due date of Assignment 3 is postponed to 11-3-2013. Students who have handed in the homework are welcomed to redeem for further modification. For detials, please come to LSB Room 228 to find Lam Ka Chun
• Lectures of Part III is over at 13-03-2013
• SPECIAL LECTURE by Dr. Y. Guo of Morgan Stanley ( Asia Pacific) at April 17 (Wed) 11:30-12:15, LT 6, LSB; all students are requested to attend !
• Lectures of Part IV is over at 03-04-2013
• A small typo for the programming assignment is updated. Problem 2(a) should be min not max.
• An update to the solution of Homework 5(b) and (c) (Thanks Ivan !)

### General Information

#### Lecturer

Shieh Narn-Rueih
Office: LSB 214    Tel: 39438900    Email:

#### Teaching Assistant

Wang Shiping
Office: LSB 222C    Tel: 39438570    Email:
Lam Ka-Chun
Office: LSB 228    Tel: 39437955    Email:

#### Time and Venue

Lecture: M9-10, LSB LT6; W4, LSB LT6
Tutorial: W3, LSB LT6

### Course Description

This is a course about the mathematics of derivative securities and options. It is designed to for those senior undergraduates and/or beginning postgraduates with some background in probability and differential equations.

The course follows the stream of Text 1, with some adapted and added materials from Text 2. It has five parts

PART I Basic Option Theory: Concept of financial markets. Call and put options. Arbitrage. Portfolios. Forward & Feature. Put-Call parity. Interests and present value. PART II Some Stochastic Tools: Normality and log-normality. Wiener process ( Brownian Motion). Ito integrals and Ito processes. Ito formula. SDEs. Geometric BM. Mean-reverting process. PART III Black-Scholes Model: Stock price as a GBM. BSM dynamics. BS pde. BS pricing formula for Eu call option. Delta-hedging. Greeks. The risk-neutrality. Stock and Eu call pricing under the risk-neutrality. General option-pricing formula under the risk-neutrality. PART VI Binomial Model and Monte Carlo for BS: CRR binomial market model. One-period. Multi-period. State price. Risk-neutrality in binomial model. Approximation to BS by binomial. Monte Carlo Method viewed from LLN and CLT in probability and its use for BS. PART V Some extensions of BS: Time-dependent BS. American put options as free boundary problem. American put option as optimal stopping problem. BS with dividends. Stochastic interest rate model. Asian option. (The last two or three in PART V may be omitted, upon the progress.)

### Textbooks

• Text 1. Raymond Chan: Lecture Notes in Financial Mathematics. CUHK Math 2011.
• Text 2. S. E. Shreve: Stochastic Calculus for Finance I & II. Springer Finance textbook, 2004.

### References

• N.-R. Shieh: Lectures Notes on Stochastic Calculus. CUHK Math 2012. This is one main material for the course Math6081 Topics in Analysis I ( Advanced Probability Theory) at Spring 2013.
• P. Wilmott , et al : The Mathematics of Financial Derivatives, a student introduction. Cambridge University Press, 1995 +.
• Kerry Back: A Course in Derivative Securities: Introduction to Theory and Computation. Springer Finance textbook, 2005.

### Assessment Scheme

 Five homework assignments 15% One programming assignment (in matlab or spreadsheet) 5% Two midterms 20% Final examination 60%