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
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
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
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
R. McDonald, Derivatives Markets (2nd Ed.)
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
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Week of |
Topic(s) |
Text Sections |
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Jan. 15 |
Review of Probability |
ch. 1 |
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Jan. 22 |
Conditioning |
ch. 2 |
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Jan. 29 |
Random Walk and Brownian Motion |
Sec. 3.1-3.5 |
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Feb. 5 |
Brownian Motion; Stochastic Calculus: Itô Integral |
Sec. 3.6-3.8, 4.1-4.3 |
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Feb. 12 |
Itô’s Lemma; Black–Scholes Equation |
Sec.4.4-4.5.3 |
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Feb. 19 |
Solution and Properties of Black–Scholes Equation; Multivariate Stochastic Calculus |
Sec. 4.5.4-4.6, 4.8 |
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Feb. 26 |
Risk-Neutral Measure: Girsanov’s Theorem, Martingale Representation Theorem, Hedging |
Sec. 5.1-5.3 |
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March 12 |
Fundamental Theorem of Asset Pricing: existence and uniqueness of Risk Neutral Measure |
Sec. 5.4 |
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March 19 |
Basic Applications to Financial Assets |
Sec. 5.5-5.7 |
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March 26 |
Connection With Partial Differential Equations |
Sec. 6.1-6.5 |
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April 2 |
Further Topics For Applying the Model |
TBD from Ch. 7-10 |
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April 9 |
Further Topics For Applying the Model |
TBD |
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April 16 |
Further Topics For Applying the Model |
TBD |
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April 23 |
Further Topics For Applying the Model |
TBD |
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Final Exam TBD week of Apr 30 to May 5 |
All |
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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 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.
Both the syllabus and the grading plan are subject to change with appropriate advance notice to the class.