Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 133: Mathematical Finance
Approved: 2006-09-01, R. Wets

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Investment Science, David Luenberger, Oxford University Press, 1998, ($84)
Search by ISBN on Amazon: 0195108094z

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

Week 1

Introduction

Cash Flow (deterministic, stochastic), math. Definition of financial instrument, examples.

Week 2

Theory of Interest

Present and future value, internal rate, evaluation criteria.

Week 3

Fixed-Income Securities

Futures market, value formulas, bonds, duration.

Week 4

Term Structure of Interest Rates

Yield curve, forward rates, expectation dynamics, floating rates bonds.

Week 5

Applied Interest Rate Analysis

Capital budgeting, optimal portfolio, dynamic cash flow process.

Week 6

Random Cash Flow

Asset return, random returns, portfolio mean and variance, Markowitz model.

Week 7

Asset Pricing Model

Market equilibrium, capital market line, capital asset pricing model (CAPM), security market, pricing formulas.

Week 8

Models and Data

Factor models, CAPM as a factor model, arbitrage pricing theory, data and statistics, estimation and calibration.

Week 9

General Principles I

Introduction, utility functions, risk aversion, utility functions and mean-variance criterion.

Week 10

General Principles II

Linear pricing, portfolio choice, finite state models, risk-neutral pricing (pricing alternatives).

Additional Notes:

Other references:
  • Pricing Derivative Securities by E. Pressman (Academic Press, 2000).
  • An Elementary Introduction to Mathematical Finance by S. Ross (Cambridge University Press, 1999).