University of Connecticut

Advanced Financial Mathematics

Math 324

Spring 2006


Classes: MWF: 1:00 – 1:50                                Instructor: James G. Bridgeman, FSA

                MSB411                                 MSB408


Office Hours: M 10:00 – 12:00                           860-486-8382                        

                       Th  10:00 –12:00                   

                       Th/F: 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


Specific Course Content

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


Required Texts

Alison Etheridge, A Course in Financial Calculus


Supplemental Material

Bass, The Basics of Financial Mathematics

Ho & Lee, The Oxford Guide to Financial Modeling



Graded Homework               40%

Paper/Project                        25%

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



  Jan. 16

Simple options and forwards; toy models; no-arbitrage principle


Jan. 23

Risk-neutral probabilities; binary trees; discrete stochastic processes


Jan. 30

Conditional expectations; martingales; markov processes; discrete stochastic integrals; equivalent martingale measure; properties of martingales

2.3-2.4, notes

Feb. 6

Compensation; binomial representation theorem; continuous limit;

definition of Brownian motion

2.4-3.1, notes

Feb. 13

Construction and properties of Brownian motion; continuous martingales

3.2-3.4, notes

Feb. 20

Properties of martingales; arbitrage and variation; stochastic integration 

3.4-4.2, notes

Feb. 27

Stochastic integration; Itô’s calculus

4.2-4.3, notes

March 13

Stochastic differential equations; more stochastic calculus; Girsanov’s Thm.

4.3-4.5, notes

March 20

Brownian martingale representation; Feynman-Kac representation;

self-financing; equivalent martingale measure; Fund. Thm. of Asset Pricing

4.6-5.1, notes

March 27

Black-Scholes; replicating portfolios; foreign exchange; dividends


April 3

Bonds; market price of risk; interest rate models

5.5-5.6, notes

April 10

Exotics; American options


April 17

Generalized Black-Scholes; multiple assets; multivariate stochastic calculus


April 24

Quantos; jump models; hedging error; stochastic volatility



Final Exam TBD week of May 1 - 6






To master the material and be prepared for the final exam you should expect to do essentially all of the exercises in the textbook.  There will be six specific assignments collected and graded, drawn mostly from the text exercises but supplemented with other questions. 




You will be expected to produce a term paper or a modeling project, due by April 26.  Details of what’s expected will be provided by a couple of weeks into the course



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