Semester | Mand. | Option | Filières |
H | x | ||
MA1, MA3 | x | ||
MA1, MA3 | x | A | |
MA1, MA3 | x | C |
Lecture | 2 weekly |
Exercises | 2 weekly |
Study plan | Semester | Mand. | Option | Filières |
Ingénierie Mathématiques 2021-22 | MA1 | x | A | |
Ingénierie Mathématiques 2021-22 | MA3 | x | A | |
Ingénierie financière 2021-22 | MA1 | x | ||
Ingénierie financière 2021-22 | MA3 | x | ||
Mathématiques 2021-22 | MA1 | x | A | |
Mathématiques 2021-22 | MA3 | x | A | |
Mineur : Ingénierie financière 2021-22 | H | x | ||
Science et ingénierie computationelles 2021-22 | MA1 | x | C | |
Science et ingénierie computationelles 2021-22 | MA3 | x | C |
Cursus | Sem. | Type |
---|---|---|
Computational science and Engineering | MA1, MA3 | Opt. |
Financial engineering minor | H | Opt. |
Financial engineering | MA1, MA3 | Opt. |
Ing.-math | MA1, MA3 | Opt. |
Mathématicien | MA1, MA3 | Opt. |
1. Brief introduction to option pricing
Basic stochastic models in finance
Basic tools of stochastic calculus
Monte Carlo simulation based methods
2. Transformation based methods
3. Density approximation techniques
4. Option pricing via PDE models
5. Gaussian processes and regression
Weight space view and function space view
Choice of covariance function and Hyper-parameters adaptation
Duality between Reproducing Kernel Hilbert Space (RKHS) and Gaussian process
Applications to derivative pricing and asset pricing
financial models, stochastic calculus, option pricing, numerical methods, Matlab, Monte Carlo simulation, PDE, Fourier transform, density approximation techniques, volatility surface, Gaussian processes, Regression
Stochastic processes / stochastic calculus
Numerical Analysis
Derivatives
Basic background in numerical analysis, linear algebra, and differential equations.
Command of Matlab.
Ex cathedra lecture, exercises in the classroom and with computer.
Attendance of lectures.
Completing exercises.
Solving problems on the computer.
60% of the grade is determined by a computer-based final examination. 40% of the grade is determined by take-home exams / graded exercises.
Hirsa, Ali. Computational methods in finance. Chapman & Hall/CRC Financial Mathematics Series. CRC Press, Boca Raton, FL, 2013.
Hilber, Norbert; Reichmann, Oleg; Schwab, Christoph; Winter, Christoph. Computational methods for quantitative finance. Springer, 2013
Seydel, Rüdiger U. Tools for computational finance. Fourth edition. Universitext. Springer-Verlag, Berlin, 2009.
Achdou, Yves; Pironneau, Olivier. Computational methods for option pricing. Frontiers in Applied
Glasserman, Paul. Monte Carlo methods in financial engineering. Springer, 2003
Björk, Tomas. Arbitrage theory in continuous time. Third edition, OUP Oxford, 2009.
Shreve, Steven E. Stochastic calculus for finance II: Continuous-Time models, Volume 11. Springer Science & Business Media, 2004.
Lamberton, Damien; Lapeyre, Bernard. Introduction to stochastic calculus applied to finance. Second revised edition. Chapman & Hall/CRC, 2008.
Williams, Christopher KI, and Carl Edward Rasmussen. Gaussian processes for machine learning. Cambridge, MA: MIT press, 2006.
Dixon, Matthew F., Igor Halperin, and Paul Bilokon. Machine Learning in Finance. Springer International Publishing, 2020.
Additional lecture material will be provided by the instructors.
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
optionnel
optionnel
Cours
Lecture
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Exercices
Exercises
Heure(s) hebdo x 14 semaines
Hour(s) per week x 14 weeks
H hebdo
H hebdo
Ecrit
Written
Session hiver
Session winter
HIV
HIV
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Balise_fin
FO_debut
[inline]=Ρ
FO_fin
HTML_debut
Ρ
HTML_fin
JS_debut
\x26#929;
JS_fin
CODE148292791
BOOLEAN_Symbol
BaliseJS_debut
\x5bepsilon\x5d
BaliseJS_fin
Balise_debut
[epsilon]
Balise_fin
FO_debut
[inline]=ε
FO_fin
HTML_debut
ε
HTML_fin
JS_debut
\x26#949;
JS_fin
CODE169976220
BOOLEAN_Symbol
BaliseJS_debut
\x5blig\x5d
BaliseJS_fin
Balise_debut
[lig]
Balise_fin
FO_debut
[inline]=›  
FO_fin
HTML_debut
›  
HTML_fin
JS_debut
\x26#x203A;\x26#160;\x26#160;
JS_fin
CODE148292899
BOOLEAN_Symbol
BaliseJS_debut
\x5bEPSILON\x5d
BaliseJS_fin
Balise_debut
[EPSILON]
Balise_fin
FO_debut
[inline]=Ε
FO_fin
HTML_debut
Ε
HTML_fin
JS_debut
\x26#917;
JS_fin
BALISETXT_SAUT
BOOLEAN_Symbol
BaliseJS_debut
\x5bbr\x2f\x5d
BaliseJS_fin
Balise_debut
[br/]
Balise_fin
FO_debut
FO_fin
HTML_debut
<br/>
HTML_fin
JS_debut
\x3cbr\x2f\x3e
JS_fin