# Derivatives pricing

llsms2225  2020-2021  Louvain-la-Neuve

Derivatives pricing
Due to the COVID-19 crisis, the information below is subject to change, in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
5 credits
30.0 h
Q1
Teacher(s)
Language
English
Prerequisites
Mathematics, informatics, probability and statistics at Bachelor level. In particular, the corresponding UCL courses are
• Mons : MQANT1110 (Mathématiques de Gestion I), MQANT1113 (Statistiques et  Probabilité), MQANT1109 (Informatique de gestion)
• LLN : LINGE1114 (Analyse), LINGE1113 (Probabilité),LINGE1225 (algorithmique et programmation en économie et gestion)
In addition, this course is reserved for students with a bachelor's degree in business engineering or students with equivalent quantitative method skills
Main themes
1. Part I: Basic probability concepts (probability space, sigma-fields, random variables, distribution, statistics and sampling via Monte Carlo).
2. Part II : Stochastic processes and related concepts.
3. Part III : random walks and Brownian motion.
4. Part IV : stochastic calculus (stochastic integrals, stochastic differential equation, Ito's lemma, Girsanov theorem)
Aims
 At the end of this learning unit, the student is able to : 1 During their programme, students of the LSM Master¿s in management or Master¿s in Business engineering will have developed the following capabilities¿ 2.2. Master highly specific knowledge in one or two areas of management : advanced and current research-based knowledge and methods.   2.4. Activate and apply the acquired knowledge accordingly to solve a problem. 3.1. Conduct a clear, structured, analytical reasoning by applying, and eventually adapting, scientifically based conceptual frameworks and models,to define and analyze a problem. 3.5. Produce, through analysis and diagnosis, implemantable solutions in context and identify priorities for action. 6.1. Work in a team : Join in and collaborate with team members. Be open and take into consideration the different points of view and ways of thinking, manage differences and conflicts constructively, accept diversity.

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Content
Fundamental mathematical concepts to understand the behavior of systems whose behavior features randomness with applications in finance.
These skills will be extensively used in LLSMS2226 (credit and interest rates risk)
Teaching methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Ex-cathedra courses enriched with exercises on R and group and/or individual projects.
Students will be asked to prepare some courses before joining the classes.
The main objective of the projects is to make the concepts more concrete and to facilitate the learining processes.
Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Continuous evaluation (projects with implementation in R)
• Date: Will be specified later
• Type of evaluation:  Report + oral presentation (teamwork, 20% of final grade) and assessment of individual contribution during the exam session (10% of final grade, see below)
Evaluation week
• Oral: No
• Written: No
Examination session
• Oral: Yes
• Written: No
• 1h preparation of questions (exercises + theory) followed by a 10 to 15 min discussion with the professor (60% of final grade)
• 10 min discussion with the teaching assistant to assess the individual contribution of the student in the group project (10% of final grade).  Attention : the grade of the project(s) (i.e. both the group and individual contributions to the project, being worth 30% of the final grade) will be set to 0 for the students who would not show up at this individual evaluation.
Bibliography
• Slides, reference books et code R
• Hassler, Stochastic Processes and Calculus: an elementary introductions with applications, Springer 2016
• Mikosh, M. Elementary Stochastic Calculus (with Finance in view), Wolrd Scientific, 1998.
• Joshi, M. : Concepts and Practice of Mathematical Finance, Cambridge University Press, 2003.
• Shreve, S. : Stochastic calculus for Finance I & II, Springer 2004.
Teaching materials
• Slides, reference books et code R
Faculty or entity

#### Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Aims
Master [120] in Economics: General