2023/2024

Degree | Type | Year | Semester |
---|---|---|---|

2500149 Mathematics | OT | 4 | 1 |

- Name:
- Albert Ferreiro Castilla
- Email:
- albert.ferreiro@uab.cat

You can check it through this link. To consult the language you will need to enter the CODE of the subject. Please note that this information is provisional until 30 November 2023.

The subject focuses on the applications of mathematical and statistics tools that have been acquired in previous courses, in particular it requires that the student has acquired the basic theoretical knowledge of calculus, calculus of probabilities, time series and numerical methods.

The objective of this course is to introduce the student to a very active area, both scientifically and professionally, such as financial mathematics. The main educational goal is to show the student the different applications of mathematical and statistical concepts in financial engineering, focusing on their proper use and interpretation of results.

Thus, the subject is set as a high-level journey by the most relevant quantitative units present in the financial industry to introduce the most fundamental economic and financial concepts and show the most commonly used techniques. From the application of time series used in macroeconomic studies, to the numerical calculation by means of Monte Carlo methods present in front offices to price financial derivatives, throughout optimization techniques in risk-return models used by fund managers and loss calculation techniques found in risk departments.

For this reason the course focuses on applications and requires the student to have acquired the basic theoretical knowledge of calculus, calculus of probabilities, time series and numerical methods.

It is also a goal that the student does a job that requires the use of the computer, and this will lead to completing the theory classes with classes of problems and case sets where the computer is present.

- Develop critical thinking and reasoning and know how to communicate it effectively, both in one's own languages and in a third language.
- Distinguish, when faced with a problem or situation, what is substantial from what is purely chance or circumstantial.
- Effectively use bibliographies and electronic resources to obtain information.
- Recognise the presence of Mathematics in other disciplines.
- Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
- Students must be capable of collecting and interpreting relevant data (usually within their area of study) in order to make statements that reflect social, scientific or ethical relevant issues.
- Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
- Students must develop the necessary learning skills to undertake further training with a high degree of autonomy.
- Understand and use mathematical language.

- Develop critical thinking and reasoning and know how to communicate it effectively, both in one's own languages and in a third language.
- Effectively use bibliographies and electronic resources to obtain information.
- Find models of the reality of a company or industry in relation to its financial or productive activity using mathematical language.
- Know how to apply the theory to specific problems or situations being worked on in practical classes.
- Know how to solve financial mathematics problems and those on other aspects related with the activities of a company or industry.
- Read specialised economic texts, both in English and in one's on language.
- Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
- Students must be capable of collecting and interpreting relevant data (usually within their area of study) in order to make statements that reflect social, scientific or ethical relevant issues.
- Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
- Students must develop the necessary learning skills to undertake further training with a high degree of autonomy.

- Introduction
- What is finance?
- Fair value and finances
- Time value of money
- Academia vs Industry: Disclaimer
- Time Series: Macroeconomic series
- ARMA, ARCH and GARCH applications
- Stochastic calculus: Valuation of financial derivatives
- Introduction to financial derivatives and their fair value
- Discrete models for the evolution of financial assets
- The continuous model as a step to the limit: the Brownian motion
- Simulation of continuous models and Monte Carlo methods
- Mathematical Optimization: Portfolio management on a risk-return framework
- Modern portfolio theory (Markowitz): risk-return framework
- Lagrange multipliers and portfolio optimization
- CAPM: Financial assets valuation model
- Probability calculus: Risk estimation
- Typology of Risks
- VaR calculations
- Financial disasters: Lessons

*Unless the requirements enforced by the health authorities demand a prioritization or reduction of these contents.*

The student acquires the scientific-technical knowledge of the subject by attending to lectures and completing it with a personal study of the topics covered. The theory classes are activities in which less interactive activity is required from the student: they are conceived as a fundamentally unidirectional method of transmitting knowledge from teacher to student.

Problems and case sets are sessions with a small number of students with a double goal. On the one hand they work the scientific-technical knowledge showed in lectures to complete their understanding and to deepen in them through a variety of activities, from the typical resolution of problems to the discussion of practitioner cases. On the other hand, the problem set activities are the natural forum in which to discuss in common the development of practitioner cases work, providing the necessary knowledge to carry it out, or indicating where and how they can be acquired. The case problem sets of this subject is proposed as a way to guide the student in a statistical fieldwork in each of its stages.

This approach is aimed at promoting active learning and developing critical reasoning and the ability to analyze and synthesize.

*The proposed teaching methodology may experience some modifications depending **on the restrictions to face-to-face activities enforced by health authorities.*

**Annotation**: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|

Type: Directed | |||

Case Studies | 20 | 0.8 | 1, 6, 10, 9, 7, 8, 4, 5, 3, 2 |

Lectures | 30 | 1.2 | 1, 6, 10, 9, 7, 8, 4, 5, 3, 2 |

Type: Supervised | |||

Tutorials | 25 | 1 | 1, 6, 10, 9, 7, 8, 4, 5, 3, 2 |

Type: Autonomous | |||

Study + Problem & Case Sets | 67.5 | 2.7 | 1, 6, 10, 9, 7, 8, 4, 5, 3, 2 |

To pass the subject it is necessary that the average of the case and problem sets is greater than or equal to 4. If the student attends the recovery exam, the final grade will be the maximum between the course grade and the weighted average of it (30 %) and the grade of the recovery exam (70%).

In the event that a student applies for Single Assessment, consisting of an Exam (50%) and an Applied Essay (50%), the student would need to obtain a mínimum of 5 in both activities to pass the subject.

*Student’s assessment may experience some modifications depending on the restrictions to face-to-face activities enforced by health authorities.*

Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|

Case Problem Sets | 35% | 2.5 | 0.1 | 1, 6, 10, 9, 7, 8, 4, 5, 3, 2 |

Case Sets | 35% | 2.5 | 0.1 | 1, 6, 10, 9, 7, 8, 4, 5, 3, 2 |

Exam | 30% | 2.5 | 0.1 | 1, 6, 10, 9, 7, 8, 4, 5, 3, 2 |

Arratia, A. (2014) Computational Finance, an introductory course with R, Atlantis Press.

Hull, J. (2008) Options, Futures, and Other Derivatives, Prentice Hall.

Ruppert, D. (2010) Statistics and Data Analysis for Financial Engineering, Springer.

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