# 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)

Search by ISBN on Amazon: 0195108094z

**Prerequisites:**

**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:**

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