# FE530 Introduction to Financial Engineering

Course Catalog Description

# Introduction

Building on mathematical models of bond and stock prices, the course leverage the two theories in different directions: Black-Scholes arbitrage pricing of options and other derivative securities on the one hand, and Markowitz portfolio optimization and the Capital Asset Pricing Model on the other hand. Models based on the principle of no-arbitrage can also be developed to study interest rates and their term structure. These are three major areas of mathematical finance, all having an enormous impact on the way modern financial markets operate. The course presents the topics at an introductory level aimed at senior undergraduate students, not only of mathematics, but also business management, finance, or economics.

**Prerequisite:** Prerequisites include elementary calculus, probability, and some linear algebra. For calculus, students are expected to have experience with derivatives and partial derivatives, finding maxima or minima of differentiable functions of one or more variables, the Taylor formula, and integrals. Topics in probability include random variables and probability distributions, in particular, the binomial and normal distributions, expectation, variance and covariance, conditional probability, and independence. Familiarity with the Central Limit Theorem would be a bonus. In linear algebra, the student should be able to solve systems of linear equations, add, multiply, transpose and invert matrices, and compute determinants. For a reference in probability theory, see Probability Through Problems by Marek
Capinski and Tomasz Jerzy Zastawniak.

Campus | Fall | Spring | Summer |
---|---|---|---|

On Campus | X | X | |

Web Campus | X | X |

Instructors

Professor | Office | |
---|---|---|

Dr. Majeed Simaan | msimaan@stevens.edu | Peirce 116 |

More Information

# Course Outcomes

After successful completion of this course, students will be able to

- Understand basic financial concepts in FE, e.g., time value of money and no-arb pricing
- Build discrete-time models, e.g., binomial trees
- Develop continuous-time models, e.g., Brownian motion
- Value different asset classes and derivatives
- Perform statistical and numerical analysis

Course Resources

# Textbook

Mathematics for Finance: An Introduction to Financial Engineering 2nd ed. 2011 Edition by Marek CapiĆski and Tomasz Zastawniak (CZ)

# Additional References

- Paul Wilmott Introduces Quantitative Finance (second edition)
- Risk Management and Financial Institutions (Wiley Finance) 4th Edition by John C. Hull
- Practical Methods of Financial Engineering and Risk Management: Tools for Modern Financial Professionals by Rupak Chatterjee

Grading

# Grading Policies

Weights | Notes | ||

1 | Exam 1 | 25% | The exam will be conducted using open-ended questions and will be held in class during the midterm. Further instructions will be distributed. |

2 | Exam 2 | 25% | The exam will be conducted using open-ended questions and will be held in class towards the end of the term. Further instructions will be distributed. |

3 | Class Project | 20% | Students are expected to work as a team and propose aproject idea by the midterm. The projects must build on the tools/ideas that are covered in the class, especially stochastic modeling. Additionally, the teams are expected to work with real data. Detailed instructions will be distributed. Presentation: upon submission, teams are expected to present their work and highlight individual contribution and synergy. Presentations will be graded on both the team and individual levels. |

4 | Homeworks | 20% | There will be two major assignments over the course of the semester. |

5 | Participation | 10% | Discussions are highly encouraged, including class attendance and general participation. Additionally, attendance will be taken over the course of the semester. |

Lecture Outline

Topic | Readings | Assignments | |
---|---|---|---|

Week 1 Jan 24, 2023 |
Introductory Class | ||

Week 2 Jan 31, 2023 |
A Simple Market Mode | Ch. 1 from CZ | Refresh probability knowledge |

Week 3 Feb 7, 2023 |
Risk-Free Assets | Ch. 2 from CZ | |

Week 4 Feb 14, 2023 |
Portfolio Management | Ch. 3 from CZ | HW1 Update |

Week 5 Feb 21, 2023 |
Forwards and Futures Contracts | Ch. 4 from CZ | |

Week 6 Feb 28, 2023 |
Midterm review | Ch. 5 from CZ | HW1 Due |

Week 7 Mar 7, 2023 |
Exam 1 | ||

Week 8 Mar 14, 2023 |
Spring Recess No class |
||

Week 9 Mar 21, 2023 |
Options: General Properties | ||

Week 10 Mar 28, 2023 |
Binomial model | Ch. 6 from CZ | Project proposal due |

Week 11 April 4, 2023 |
Binomial Model 2 | Ch. 6 from CZ | |

Week 12 April 11, 2023 |
Continuous Time Model | Ch. 8 from CZ | HW2 Update |

Week 13 April 18, 2023 |
Black-Scholes Model | Ch. 8 from CZ | |

Week 14 April 25, 2023 |
Final Review + Guest Speaker | HW2 Due | |

Week 15 May 2, 2023 |
Project Presentation | Final Project Due | |

Week 16 May 9, 2023 |
Exam II |