MA 547 Financial Mathematics
Spring, 2011           T, Th 11:45am-1:00pm               RD 339
http://www4.ncsu.edu/~tpang/MA547/MA547.html

1.  Instructor:            Tao Pang                     Office:             SAS Hall 4116
    Telephone:             513-2110                      Email:              tpang@ncsu.edu
   Office hours:          Tuesday, 10:00am-11:00am;

Thursday, 2:30pm-3:15pm or by appointment.

2. Prerequisites: Introduction to Probability and Stochastic Processes (MA (ST) 546) or basic probability theory and calculus. Some knowledge of MATLAB is welcome but not required.

3. Textbooks:

-        A Course in Financial Calculus, by Alison Etheridge, Cambridge University Press (2002). Required.

4. Outline of Course:

-   Introduction to financial derivatives. Pricing and hedging problems.

-   One-period and multi-period models. The essential concepts and tools in discrete cases.

-   Review of discrete probability spaces and fundamental results on martingale theory. Optimal stopping problem applied to American options.

-   Limit theorems: from discrete to continuous time models.

-   Brownian motion and the associated Ito's Stochastic Calculus.

-   Pricing derivatives (European, American, Asian,...) in the context of continuous models such as Black-Scholes.

-   Relation with PDE's and numerical issues.

-   Models for interest rates and portfolio management problems (if time permits).      

5. Grade Policy

-   Homework: 10%

-   Midterm Exams: 50%

·         Two in-class midterm exams will be given on Feb. 15th, Tuesday and April 5th, Tuesday. Dates are tentative.

·         Each exam will cover the topics studied in classes before the exam and after the last exam, if any.

-   Final Exam: 40%

·         Exam time: May 10th, Tuesday, 8:00am-11:00am.

·         It will cover the work of the entire semester. 

6. Further Readings:

-       Mathematics:

o       B. Oksendal - Stochastic Differential Equations: An Introduction with Applications, 6 edition (2005)

o       I. Karatzas and S. Shreve - Brownian Motion and Stochastic Calculus, 2 edition (2006), Springer, Graduate Texts in Math. 113.

-       Mathematics and Finance:

o       M. Musiela and M. Rutkowski - Martingale Methods in Financial Modeling, Springer (1997), Applications of Mathematics 36.

o       D. Lamberton and B. Lapeyre - Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall / CRC (1996).

o       I. Karatzas and S. Shreve - Methods of Mathematical Finance, Springer (1998), Applications of Mathematics 39.

o       P. Wilmott, S. Howison and J. Dewynne - The Mathematics of Financial Derivatives, Cambridge University Press (1995).

o       Fouque-Papanicolaou-Sircar, Derivatives in Financial Markets with Stochastic Volatility,  Cambridge University Press (2000).

-       Finance:

o       J. Hull - Options, Futures and Other Derivatives, 6 edition (2005), Prentice Hall Press.

o       M. Baxter and A. Rennie - Financial Calculus - An introduction to derivative pricing, Cambridge University Press (1996).

o       D. Duffie - Dynamic Asset Pricing Theory, 2nd ed. (1996) Princeton University Press.

7. Attendance Policy
The attendance policy is consistent with the Academic Regulations which can be found at http://www.ncsu.edu/policies/academic_affairs/courses_undergrad/REG02.20.3.php

8. Academic Integrity
Plagiarism and cheating are attacks on the very foundation of academic life, and cannot be tolerated within universities. Section eight (8) of the Code defines academic dishonesty and provides information on potential sanctions for violators of academic integrity. The NCSU Academic Integrity statement can be found at http://www.ncsu.edu/policies/student_services/student_discipline/POL11.35.1.php

9. Disability Services for Students
Students with a disability must contact the NCSU Disability Services.
Additional information: http://www.ncsu.edu/equal_op/dss/.