Machine learning is a scientific discipline that is concerned with the design and development of algorithms that allow computers to learn from data. A major focus of machine learning is to automatically learn complex patterns and to make intelligent decisions based on them. The set of possible data inputs that feed a learning task can be very large and diverse, which makes modelling and prior assumptions critical problems for the design of relevant algorithms.
This course focuses on the methodology underlying supervised and unsupervised learning, with a particular emphasis on the mathematical formulation of algorithms, and the way they can be implemented and used in practice. We will therefore describe some necessary tools from optimization theory, and explain how to use them for machine learning. Numerical illustrations will be given for most of the studied methods

MAP542 Numerical processing of financial data
 
We will start with a short tutorial on Pandas with examples based on financial data.
 
The course will tackle the following topics:
 
· Sequential data in one dimension (main example: equity indices - SP500, Eurostoxx) : missing values, missing dates, interpolation. Estimation of volatilities, autocorrelations.
· Sequential data multi-dimensional : correlations, scarcity of data for high dimensional correlations estimation, inversion of covariance matrices.
· Order book data : volumes, information at bid and ask sides, slippage, market impact of a trade (data: order books on cryptocurrencies)
· Yield curves reconstruction/interpolation : from bonds, from futures (e.g. on cryptocurrency).
· Options data :
  • option prices (on large equity index such as SP500), reconstruction of forward and discount factor from put-call parity.
  • Black Scholes formula with some justification (without continuous time stochastic calculus), computation of implied volatilities (bisection method, Newton method).
  • Static no-arbitrage conditions on option prices and implied volatilities, fitting of a parametric implied volatility smile (SVI, SSVI).

Langue du cours : Anglais