|
|
Main menu for Browse IS/STAG
Course info
KMA / SF
:
Course description
Department/Unit / Abbreviation
|
KMA
/
SF
|
Academic Year
|
2023/2024
|
Academic Year
|
2023/2024
|
Title
|
Stochastic Finance
|
Form of course completion
|
Exam
|
Form of course completion
|
Exam
|
Accredited / Credits
|
Yes,
6
Cred.
|
Type of completion
|
Combined
|
Type of completion
|
Combined
|
Time requirements
|
Lecture
3
[Hours/Week]
Practice
2
[Hours/Week]
|
Course credit prior to examination
|
Yes
|
Course credit prior to examination
|
Yes
|
Automatic acceptance of credit before examination
|
No
|
Included in study average
|
YES
|
Language of instruction
|
Czech, English
|
Occ/max
|
|
|
|
Automatic acceptance of credit before examination
|
No
|
Summer semester
|
0 / -
|
0 / -
|
2 / -
|
Included in study average
|
YES
|
Winter semester
|
0 / -
|
0 / -
|
0 / -
|
Repeated registration
|
NO
|
Repeated registration
|
NO
|
Timetable
|
Yes
|
Semester taught
|
Summer semester
|
Semester taught
|
Summer semester
|
Minimum (B + C) students
|
not determined
|
Optional course |
Yes
|
Optional course
|
Yes
|
Language of instruction
|
Czech, English
|
Internship duration
|
0
|
No. of hours of on-premise lessons |
|
Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
|
Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
|
Fundamental theoretical course |
No
|
Fundamental course |
No
|
Fundamental theoretical course |
No
|
Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
|
None
|
Preclusive courses
|
N/A
|
Prerequisite courses
|
N/A
|
Informally recommended courses
|
N/A
|
Courses depending on this Course
|
N/A
|
Histogram of students' grades over the years:
Graphic PNG
,
XLS
|
Course objectives:
|
The aim of this course is to introduce basic tools of stochastic calculus and analysis in mathematical finance and their application to different continuous-time market models and to selected financial derivatives.
|
Requirements on student
|
Students have to work out all assignments or lab problems and tests given throughout the term and get at least 60%. Assignments are both of theoretical and practical character, in particular students have to be prepared to use real market data and implement studied models in a suitable software (e.g. MATLAB). Final examination consists of written and oral part and students are required to get at least 60% in both parts.
|
Content
|
1. Motivation, revision of probability theory and fundamentals of portfolio theory and financial derivatives - binomial asset pricing model.
2. Introduction to stochastic calculus - Wiener process, stochastic integral, Itô lemma and its applications.
3. Advanced parts of stochastic calculus - martingales, change of measure, stochastic differential equations, stopping times.
4. Market models I. Black-Scholes model, pricing partial differential equations and their solutions, implied volatility surfaces.
5. Financial derivatives I. Futures, European and American options, brief review of some exotic financial derivatives.
6. Market models II. Interest rate (short-rate) models, Vašíček model, Cox-Ingersoll-Ross model, bonds and swaps.
7. Market models III. Multidimensional models, HJM modelling framework, forward rates, no-arbitrage condition and Libor market models.
8. Financial derivatives II. Forwards, swaptions, caps, caplets.
9. Numerical solution of stochastic differential equations - theory and application to selected models, Monte Carlo simulations.
10. Advanced topics in financial modelling - stochastic volatility models, jump-diffusions, robust pricing.
|
Activities
|
|
Fields of study
|
Všechny podstatné informace a studijní materiály jsou k dispozici na almaMATHer.
All important information and study materials are available at almaMATHer.
|
Guarantors and lecturers
|
|
Literature
|
-
Basic:
Shreve, Steven E. Stochastic calculus for finance. I, The binomial asset pricing model. New York : Springer, 2004. ISBN 0-387-40100-8.
-
Basic:
Shreve, Steven E. Stochastic calculus for finance. II, Continuous-time models. New York : Springer, 2004. ISBN 0-387-40101-6.
-
Recommended:
Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. New York : Springer-Verlag, 1999. ISBN 0-387-97655-8.
-
Recommended:
Baxter, Martin; Rennie, Andrew. Financial calculus : an introduction to derivative pricing. Cambridge : Cambridge University Press, 1996. ISBN 0-521-55289-3.
-
Recommended:
Hull, John C. Options, Futures, and Other Derivatives. Pearson, 2015. ISBN 978-0133456318.
-
Recommended:
Wilmott, Paul. Paul Wilmott on Quantitative Finance. 2nd ed. Chichester : John Wiley & Sons, 2006.
-
Recommended:
Oksendal, Bernt. Stochastic differential equations : an introduction with applications. Berlin : Springer, 2000. ISBN 3-540-63720-6.
-
Recommended:
Maslowski, Bohdan. Stochastic Equations and Stochastic Methods in PDE's. Plzeň, 2006.
-
On-line library catalogues
|
Time requirements
|
All forms of study
|
Activities
|
Time requirements for activity [h]
|
Preparation for comprehensive test (10-40)
|
25
|
Individual project (40)
|
25
|
Contact hours
|
65
|
Preparation for an examination (30-60)
|
42
|
Total
|
157
|
|
Prerequisites
|
Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
aktivně ovládat teorii generování (pseudo) náhodných čísel a znát markovskou vlastnost náhodných procesů |
definovat a vysvětlit klíčové pojmy a nástroje z teorie pravděpodobnosti (v rozsahu základního kurzu KMA/PSA) |
definovat a vysvětlit teorii obyčejných diferenciálních rovnic prvního řádu, jak lineárních, tak obecně nelineárních |
ovládat teorii náhodných procesů s diskrétním stavovým prostorem (v rozsahu předmětu KMA/ZNP) |
popsat základní pojmy a principy používané ve finanční sféře (typy diskontování, úrokové míry apod.) |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
aplikovat metody řešení diferenciálních rovnic pro počáteční úlohy |
generovat náhodné vektory z různých rozdělení ve vhodném SW (např. Matlab, R) |
použít vztahy mezi funkcí hustoty a distribuční funkcí, střední hodnotou, rozptylem náhodné veličiny |
použít vztahy mezi obecným, partikulárním a homogenním řešením obyčejné diferenciální rovnice |
použít základní statistické metody k odhadování vlastností náhodných veličin |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
|
Learning outcomes
|
Knowledge - knowledge resulting from the course: |
formulovat a vysvětlit fundamentální věty oceňování derivátů |
ovládat aparát stochastického kalkulu pro účely finančních modelů |
ovládat základní numerické metody (např. Euler-Maruyama) řešení stochastických diferenciálních rovnic |
popsat a rozlišit základní evoluční modely se stochastickou dynamikou, které se používají jako modely finančních trhů |
popsat základní finanční deriváty a odvodit jejich matematický popis |
popsat základní matematicko-finanční úlohy a jejich matematickou formulaci |
Skills - skills resulting from the course: |
aplikovat teoretické znalosti Itôova kalkulu, především na řešení stochastických diferenciálních rovnic |
implementovat oceňovací vztahy a numerické metody pro simulaci základních finančních modelů ve vhodném SW (např. Matlab, R) |
odvodit základní vztahy pro vybrané vlastnosti základních finančních modelů |
samostatně zpracovat práci na vybrané téma |
Competences - competences resulting from the course: |
N/A |
N/A |
|
Assessment methods
|
Knowledge - knowledge achieved by taking this course are verified by the following means: |
Written exam |
Oral exam |
Skills - skills achieved by taking this course are verified by the following means: |
Written exam |
Skills demonstration during practicum |
Seminar work |
Competences - competence achieved by taking this course are verified by the following means: |
Written exam |
Oral exam |
Seminar work |
|
Teaching methods
|
Knowledge - the following training methods are used to achieve the required knowledge: |
Interactive lecture |
Lecture supplemented with a discussion |
Self-study of literature |
Skills - the following training methods are used to achieve the required skills: |
Interactive lecture |
Task-based study method |
Practicum |
Individual study |
Competences - the following training methods are used to achieve the required competences: |
Self-study of literature |
Task-based study method |
Individual study |
|
|
|
|