Type of Credit: Required
Credit(s)
Number of Students
This course provides students the background mathematical knowledge for the valuation of standard and complex derivatives.
These mathmatical knowledges will enable students to price and hedge risks as well as to design new derivative products.
能力項目說明
This course provides graduate students in financial engineering the required tools for advanced research in the valuation of derivatives.
The subjects include probability theory, stochastic processes, stochastic calculus and their applications in the valuation of various derivatives.
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
No. Date Chapter Subjects and Assignments
1 09/11 Introduction
2 09/18 Probability theory
3 09/25 Probability theory
4 10/02 Information and filtered probability space
5 10/09 Conditional expectations
6 10/16 Brownian motion
7 10/23 First passage time
8 10/30 Stochastic calculus
9 11/06 Midterm examination
10 11/13 Ito's formula
11 11/20 Black-Scholes-Merton equation
12 12/27 Risk-neutral pricing
13 12/04 Fundamental theorems of pricing
14 12/11 Partial differential equations
15 12/18 Exotic options
16 12/25 American options and change of measure
17 01/01 American options and change of measure
18 01/08 Final examination
Final tests, --------------------------------- 45 %
Mid-term examination------------------- - 30%
Evaluation and/or Homework -------- ---- 25%
Total 100%
1. Shreve, S.E., Stochastic Calculus for Finance II Continuous-Time Models, Springer-Verlag, NY, 2004. (Textbook)
2. Musiela, M. and Rutkowski, M., Martingale Methods in Financial Modelling, Springer-Verlag, NY, 1997. (Reference)