University of Connecticut

Advanced Financial Mathematics

Math 324

Spring 2008

Classes:W: 2:00 – 2:50 MSB411 Instructor: James G. Bridgeman, FSA

F: 1:00 – 2:50 BRON124 MSB408

Office Hours: M/Th 10:00 – 11:00 860-486-8382

W 11:00 –12:00 bridgeman@math.uconn.edu

Th 2:00 – 3:00 websites: instructor’s: www.math.uconn.edu/~bridgeman/index.htm

Or by appointment course: www.math.uconn.edu/~bridgeman/math324s08/index.htm

Context for the Course

Required for the Professional Master’s degree in Applied Financial Mathematics; contains material relevant for SOA exams MFE and C

Specific Course Content

The Standard Models for Pricing and Replicating Financial Instruments (such as Derivatives) Presented Within the Context of the Theory of Continuous Stochastic Processes and Stochastic Calculus

Required Text

Steven Shreve, Stochastic Calculus for Finance II- Continuous Time Models, Springer 2004

Note errata posted at www.math.cmu.edu/users/shreve/ErrataVolIISep06.pdf; and More errata for 2004 printing of Volume II, July 2007

Supplemental Material (not required)

Richard Bass, The Basics of Financial Mathematics (highly recommended)

www.math.uconn.edu/~bass/finlmath.pdf

Alison Etheridge, A Course in Financial Calculus, Cambridge 2002

Steven Shreve, Stochastic Calculus for Finance I- The Binomial Asset Pricing Model, Springer 2004

Ho & Lee, The Oxford Guide to Financial Modeling, Oxford 2004

R. McDonald, Derivatives Markets (2^nd Ed.), Pearson Addison-Wesley 2006

Brigo & Mercurio, Interest Rate Models-Theory and Practice (2^nd Ed.,3^rd printing), Springer 2007

Grading

Take-home Tests 30%

Paper/Project 35%

Final Exam 35%

Both the syllabus and the grading plan are subject to change with appropriate advance notice to the class.

Outline & Intended Pace
Week of	Topic(s)	Text Sections
Jan. 21	Main Ideas: Risk-Neutral Pricing & Hedging Binomial Example; What’s Needed To Generalize Review of Probability - Basics	ch. 1
Jan. 28	Review of Probability – Expectations, Convergence, Change of Measure	ch. 1
Feb. 4	Information, Filtrations, Independence, Conditioning	ch. 2
Feb. 11	Random Walk and Brownian Motion	Sec. 3.1-3.3
Feb. 18	Properties of Brownian Motion	Sec. 3.4-3.8
Feb. 25	Stochastic Calculus: Itô’s Integral, Itô’s Lemma	Sec. 4.1-4.4.1
March 3	General Itô Lemma; Black–Scholes Equation	Sec. 4.4.2-4.5
March 17	Multivariate Stochastic Calculus; Levy’s Criterion Girsanov’s Theorem: Risk-Neutral Measure, Black-Scholes Formula	Sec. 4.6, 4.8 Sec. 5.1-5.2
March 24	Martingale Representation Theorem: Hedging Fundamental Theorems of Asset Pricing: existence and uniqueness of Risk Neutral Measure	Sec. 5.3-5.4
March 31	Basic Applications to Financial Assets	Sec. 5.5-5.7
April 7	Stochastic Differential Equations; Feynman-Kac Thm.	Sec. 6.1-6.6
April 14	Further Topics For Applying the Model	TBD from Ch. 7-10
April 21	Further Topics For Applying the Model	TBD
April 28	Further Topics For Applying the Model	TBD
	Final Exam TBD week of May 5 to May 10	All

Homework

To master the material and be prepared for the final exam you should expect to do most of the exercises in the textbook as part of your studying each chapter. Specific exercises will be assigned and they are fair game for the final exam. These will not be collected and graded so it’s up to you to ask questions about the ones you don’t feel comfortable with.

Take Home Tests

There will be two or three take home tests given and graded over the course of the semester, at about the level of difficulty of the text exercises and sometimes drawn directly from the text exercises.

Paper/Project

You will be expected to produce a term paper or a modeling project, due by April 30. This can be a topic that you select from chapters 7 thru 10, or a project that goes beyond what the text presents on a topic covered in chapters 1 thru 6. If you can’t come up with a topic that interests you, one will be assigned.