MAP542 - Numerical processing of financial data (2022-2023)

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).