Title in French: Mathématiques et statistiques pour la finance
Course code: tba
ECTS credits: 2
Teaching hours: 50h
Language of instruction: English
Coordinator: Christophe Pouet
Instructors: Sébastien Darses, Christophe Pouet
Brief description
This course is a ground course for anyone interested in quantitative finance. It is split into two parts. The first part is devoted to stochastic calculus and Black-Scholes model. It introduces the mainstream mathematical and probabilistic tools for derivatives pricing. The second part called Introduction to econometrics is devoted to the analysis of time series and related tools.
Learning outcomes
Master the notion of stochastic process (in particular Brownian motion)
Use it to value (simple) financial assets
Know the main models of time series
Use it to model financial series
Course content
Stochastic calculus and introduction to mathematical finance
Brownian motion: Definition and properties
Stochastic integrals: Itô integral, Itô formula, Girsanov theorem
Stochastic differential equations: existence and uniqueness of a solution
Link with parabolic PDE: Feynman-Kac formula
Black-Scholes model: pricing of european options
Introduction to econometrics: time series analysis
Theory for SARIMA models
Identification statistical tools: autocorrelation function, partial autocorrelation function, spectral density
Parameter estimation and their asymptotic distribution
Model hypothesis checking: homoskedasticity vs heteroskedasticity, residual randomness and gaussianity
Forecasting using SARIMA models
Bibliography
Lamberton, D. and B. Lapeyre, “Introduction to Stochastic Calculus Applied to Finance”, 2nd ed., Chapman and Hall/CRC, 2007