# ELE 3911 Introduction to Quantitative Finance

## ELE 3911 Introduction to Quantitative Finance

Quantitative finance is an exciting field where we apply mathematics, statistics, and computing to solve financial problems. The main finance areas where advanced quantitative techniques are applied are derivative securities (pricing and hedging), risk management, and portfolio management. This course introduces the fundamental mathematical and statistical tools of quantitative finance in a mathematically rigorous way, with applications. The core aims are the analysis of financial variables, the modeling of uncertainty and risk, and the building of market models for pricing and portfolio choices.

The students by the end of the course will know:

- The fundamental probability theory and statistics underlying the modelling of uncertainty in finance
- The fundamentals of matrix algebra and vector spaces as used for modelling multivariate structures or series
- The theory of linear regression analysis
- Models of financial time series
- Market models and the notion of no arbitrage and replication

The students by the end of the course will be able to

- Model the time-value of money and analytically compute present and future values
- Model uncertainty in financial markets using various models and approaches
- Simulate univariate and multivariate financial time series using Monte Carlo simulations
- Construct discrete-time market models for pricing derivative securities

The students by the end of the course will be able to choose, analyze rigorously, and implement appropriate models of financial variables, depending on the problem at hand.

The plan of the course (subject to time availability) is as follows, where Miller and C&Z (Capinski and Zastawniak) refer to the two compulsory textbooks:

- Basic math and the time-value of money: Miller ch.1 and C&Z ch. 2.
- Review of basic probability and statistics: Miller ch.2 & 3.
- Distributions: Miller ch. 4 & 5 (excluding Copulas).
- Bayesian analysis: Miller ch. 6.
- Hypothesis testing and confidence intervals: Miller ch. 7.
- Matrix algebra: Miller ch. 8.
- Vector spaces: Miller ch. 9.
- Linear regression analysis: Miller ch. 10.
- Time-series models: Miller ch. 11.
- A simple market model: C&Z ch.1.
- Risky assets: C&Z ch. 3.
- Discrete-time market models: C&Z ch. 4.

The course contains lecturing, solving problems in class, and implementation in R.

The course can be used as a preparation course for the Master's programs.

Higher Education Entrance Qualification

**Disclaimer**

Deviations in teaching and exams may occur if external conditions or unforeseen events call for this.

Basic courses in Mathematics, Statistics and Finance.

Assessments |
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Exam category: Submission Form of assessment: Written submission Weight: 20 Grouping: Group/Individual (1 - 2) Duration: 1 Semester(s) Comment: One or more assignments with data analysis and model implementation in R. Exam code: ELE 39111 Grading scale: Point scale leading to ECTS letter grade Resit: All components must, as a main rule, be retaken during next scheduled course |

Exam category: Submission Form of assessment: Written submission Invigilation Weight: 80 Grouping: Individual Support materials: - BI-approved exam calculator
- Simple calculator
- Bilingual dictionary
- Monolingual dictionary, English-English
Duration: 4 Hour(s) Comment: Individual final exam. Exam code: ELE 39111 Grading scale: Point scale leading to ECTS letter grade Resit: All components must, as a main rule, be retaken during next scheduled course |

Activity | Duration | Comment |
---|---|---|

Teaching | 45 Hour(s) | |

Student's own work with learning resources | 100 Hour(s) | |

Group work / Assignments | 51 | |

Examination | 4 Hour(s) |

A course of 1 ECTS credit corresponds to a workload of 26-30 hours. Therefore a course of 7,5 ECTS credit corresponds to a workload of at least 200 hours.