Office: LSB 214 Tel: 39438900 Email:
Office: LSB 222C Tel: 39438570 Email:
Office: LSB 228 Tel: 39437955 Email:
Time and Venue
|Lecture: M9-10, LSB LT6; W4, LSB LT6|
|Tutorial: W3, LSB LT6|
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.)
|Five homework assignments||15%|
|One programming assignment (in matlab or spreadsheet)||5%|
The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:http://www.cuhk.edu.hk/policy/academichonesty/
and thereby help avoid any practice that would not be acceptable.