University of Connecticut

Advanced Financial Mathematics

Math 324

Spring 2007

Classes:W: 2:05 – 2:50 MSB307 Instructor: James G. Bridgeman, FSA

F: 1:00 – 2:45 TLS 301 MSB408

Office Hours: M 10:00 – 11:00,1:00-2:00 860-486-8382

Th 10:00 –12:00,2:00-3:00 bridgeman@math.uconn.edu

F 10:00 –11:00 websites: instructor’s math.uconn.edu/~bridgeman

Or by appointment course: math.uconn.edu/~bridgeman/math324s07/index.html

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 Texts

Steven Shreve, Stochastic Calculus for Finance II

Note errata posted at www.math.cmu.edu/users/shreve/ErrataVolIISep06.pdf; and www.math.cmu.edu/users/shreve/ErrataVolIINov06.pdf

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

Steven Shreve, Stochastic Calculus for Finance I

Ho & Lee, The Oxford Guide to Financial Modeling

R. McDonald, Derivatives Markets (2^nd Ed.)

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. 15	Review of Probability	ch. 1
Jan. 22	Conditioning	ch. 2
Jan. 29	Random Walk and Brownian Motion	Sec. 3.1-3.5
Feb. 5	Brownian Motion; Stochastic Calculus: Itô Integral	Sec. 3.6-3.8, 4.1-4.3
Feb. 12	Itô’s Lemma; Black–Scholes Equation	Sec.4.4-4.5.3
Feb. 19	Solution and Properties of Black–Scholes Equation; Multivariate Stochastic Calculus	Sec. 4.5.4-4.6, 4.8
Feb. 26	Risk-Neutral Measure: Girsanov’s Theorem, Martingale Representation Theorem, Hedging	Sec. 5.1-5.3
March 12	Fundamental Theorem of Asset Pricing: existence and uniqueness of Risk Neutral Measure	Sec. 5.4
March 19	Basic Applications to Financial Assets	Sec. 5.5-5.7
March 26	Connection With Partial Differential Equations	Sec. 6.1-6.5
April 2	Further Topics For Applying the Model	TBD from Ch. 7-10
April 9	Further Topics For Applying the Model	TBD
April 16	Further Topics For Applying the Model	TBD
April 23	Further Topics For Applying the Model	TBD
	Final Exam TBD week of Apr 30 to May 5	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 the parts of the text that we don’t cover or one that goes beyond the level at which we do cover something. If you can’t come up with a topic that interests you, one will be assigned.