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

                         Th  2:00 – 3:00          websites: instructor’s:

                       Or by appointment                      course:

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; and More errata for 2004 printing of Volume II, July 2007


Supplemental Material (not required)

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

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 (2nd Ed.), Pearson Addison-Wesley 2006

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



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


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


April 28

Further Topics For Applying the Model



Final Exam TBD week of May 5 to May 10






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. 




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.



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