Homepage of MATH 194

Winter 2006

Department of Mathematics

University of California San Diego

COURSE INFORMATION SHEET

Instructor Contact Information is posted on her homepage

Teaching Assistant

…      Nam Lee, nhlee@math.ucsd.edu

…      Office Hours: Tuesdays 4pm-5:30pm, AP&M 2402

…      Finals Week Office Hours: Monday 4pm –5pm, AP&M 2402

LECTURES

…      Week 1:

o     Introduction to Financial Markets

o     Definition of the Single Period Binomial (CRR) Model

o     Arbitrage and Replicating Strategies (for the Single Period CRR Model)

…      Week 2:

o     The Risk Neutral Probability, Manufacturing Cost Lemma, and the Fundamental Theorem of Asset Pricing (for the Single Period CRR Model).

o     Definition of the Multi-Period Binomial Model

o     Single Period Binomial Model Lecture Review List

…      Week 3:

o     Trading in the Market: Feasible, Self-Financing, Replicating Strategies

o     Risk Neutral Property and Conditional Expected Value

…      Week 4:

o     Properties of Conditional Expected Value

o     Exam 1: Through Homework 4 and Week 3 Lectures.

…      Week 5:

o     Risk Neutral Property and Martingales; The Fundamental Theorem of Asset Pricing for the ECC.

o     Multiperiod Binomial Model Lecture Review List

…      Week 6:  American Contingent Claims (ACC):

1.   Definition and Properties of the Superhedging Strategies (pages 19-22)

2.   Definition of Snell Envelop (top page 23) Concept Check Worksheet

3.   Definitions of Arbitrage Opportunities (Bottom page 25-top page 26)

4.   Constructing Arbitrage Opportunities (top page 27)

…      Week 7: American Contingent Claims (ACC):

o     Arbitrage Free Pricing for ACC (bottom page 27-28).  We will prove the necessary supporting facts using a different approach than the textbook.  In particular, you do not need to study Lemmas 2.3.1 and Lemma 2.3.2.  However, you do need to know Doobís stopping theorem.

o     Updated Multi-period Binomial Model Lecture Review List (includes ACC).

…      Week 8:

o     Overview of Finite Market Model

o     Exam 2: Through Homework 8 and Week 7 Lectures

HOMEWORK

…      Homework 1: Due Friday, 1/13

…      Homework 2: Due Wednesday, 1/18

…      Homework 3: Due Wednesday, 1/25

…      Homework 4: Due Wednesday, 2/1 (Students may want to make a photocopy for exam study purposes.)

…      Homework 5: Due Wednesday, 2/8

…      Homework 6: Due Wednesday, 2/15

…      Homework 7: Due Wednesday, 2/22

…      Homework 8: Due Wednesday, 3/1 (Students may want to make a photocopy for exam study purposes.)

…      Homework 9: Due Wednesday, 3/8

1.   Problem 2 from Section 3.7 of the textbook

2.   Bonus: Problem 1 from Section 3.7 of the textbook.  The rules are that the bonus problem must be solved using only your own brain and the textbook, i.e., not consulting myself, the TA, or other resources.  You may collaborate with your classmates, in which case the points will be shared equally among the collaborators.  In order to get credit, you or you and your collaborators must present your solution to me in my office hours, or by appointment by Friday, 3/10.  Note: You may not share your ideas/work with anyone in the course, except those identified as collaborators.

…      Homework 10:  Due Wednesday, 3/15

1.   For Problem 2 from Section 3.7 of the textbook please answer the following.

1.   Is the market complete?  Explain.

2.   Use the Manufacturing Cost Lemma to compute the arbitrage free price process.

2.   Problem 3 from Section 3.7 of the textbook.  In part (b), for both choices of r comment on whether or not the market is complete.

3.   Problem 4 from Section 3.7 of the textbook.  Add part (iv), which is to determine if the market is complete.