Textbook: Steven E. Shreve, Stochastic Calculus for Finance, Volume I: The Binomial Asset Pricing Model, Springer, ca. 30$
Tentative syllabus: We will depart from the department syllabus somewhat. We focus on the binomial asset pricing model, as found in the Shreve textbook, plus some topics that illustrate the use of optimization methods in finance.
1. Interest rates
2. Portfolios, convex geometry, and optimization
3. Review of basic probability theory
4. Derivative securities, the European call option, in the one-period model
5. Arbitrages and no-arbitrage pricing theory
6. Replication
7. Risk neutrality
8. Multi-period binomial model.
9. Dynamic programming compression.
10. Replication in the multi-period model.
11. Conditional expectations.
12. Discrete-time stochastic processes.
13. Markov processes.
14. Martingales.
15. Lookback options. Two-dimensional Markov processes and dynamic programming compression.
16. Asian call options. Lack of dynamic programming compression in the generic Asian call option.
17. American options.
18. Replication and supermartingales.
19. Random times and stopping times.
20. General American derivatives and optimal exercise.
Grading: Homework 30%, Midterm 30%, Final 40%. The lowest grade of the homework series will be dropped. There will be two midterms. The lowest grade of the two midterms will be dropped.
Homework will be assigned, and other announcements will be made, via SmartSite. Auditors, let me know and I will give you access to the course materials on SmartSite.
Exam Dates:
Midterm 1 (in class): May 3 (Fri)
Midterm 2 (in class): May 22 (Wed)
Final -- as announced on MyUCDavis
Class computer accounts: Some homework will be computer-based. You will need class accounts; to create one, please go to: http://www.math.ucdavis.edu/comp/class-accts