Contents

Modules

Aims

Stochastic modeling and derivatives

Course and small classes

Emmanuel Gobet, PR. Ecole Polytechnique

 Aim : master the up-to-date tools for stochastic modeling used in pricing/hedging derivatives, calibratiing models, managing and modeling risks.

Content :

  • Financial derivatives, future and forward contracts, spot markets, no-arbitrage arguments, static hedging of vanilla options with call/puts
  • Dynamics hedging portolio, change of numeraire, PDE valuation, Black-Scholes formula and ramifications
  • Local and stochastic volatility, Dupire model, Heston model, Gyongy projection
    Implied volatility, dynamics of IV, links with spot volatility, hedging and sticky rules, robustness formulas
  • Asymptotics for prices and implied volatility (small maturity, small vol of vol, large strikes, wing’s formula…)
  • Interest rates modeling, HJM framework, Gaussian model, market models
  • FX markets, cross-currency derivatives

Evaluation : written final exam + pricing/calibration project joint with “Numerical methods”.

Acquired skills : In-depth understanding of stochastic models  dynamics of traded assets, inetrest rates, etc, and their use for the pricing of derivative products and risk management.

Numerical methods : efficient Monte Carlo

Course and small classes

Gilles Pages, PR. Sorbonne Université

Aim : Provide fast efficient simulation methods for pricing and hedging derivatives on various asset classes, risk management, model validation.

Content :

  • Random variate simulation: yield and complexity
  • Variance réduction
  • Numerical schemes for stochastic dynamics : which scheme for which problem ?
  • Quasi-Monte Carlo versus Monte Carlo
  • Erasing the bias: multilevel mehods
  • Efficient implémentation on modern device (GPU)

Evaluation : written final exam + computing project joint with « Stochastic Calculus & Control ou Derivatives.

Acquired skills : Optimize the implementation of a Monte Carlo simulation method under operational constraints.

Statistical Methods and Data Science for Finance

Course and small classes

Mathieu Rosenbaum, PR. Ecole Polytechnique

Aim : Introduction to standard statistical methods for risk management.

Content :

  • Markowitz theory and capital asset pricing model
  • Principal component analysis
  • Random matrices
  • High dimensional regression methods
  • Copulas
  • GARCH models

Evaluation : Take home QCM + computing project joint with « Derivatives”.

Acquired skills : Estimation techniques for portfolio management, Econometrics of high dimensional data,
Risk modelling and forecasting.

Stochastic calculus and control theory

Course and small classes

Nizar Touzi, PR. Ecole Polytechnique

Aim : Basics of stochastic calculus tools for finacial modeling, Hamilton-Jacobi-Bellman equations for control problems, applications in hedging and portfolio optimization.

Content :

  • Brownian motion, stochastic integral, Itô’s formula, Girsanov’s change of measure, review of basic valuation theory, Poisson process, financial modeling with jumps
  • Optimal stochastic control and HJB equation, application to portfolio optimization
  • Optimal stopping and obstacle partial differential equation, applcation to American securities
  • Introduction to stochastic differential games, application to contract theory

Evaluation : Take home QCM + computing project joint with « Numerical methods”.

Acquired skills : Stochastic modeling, optimization under uncertainty, nonlinear partial differential equations.

Professional seminars/meetings

 

Modules

Aims

Regulation

Course and small classes

Michael Vincent, Sorbonne Université

AIM : Introduction to regulation starting from a historical viewpoint.

Content :

  • 1929 crisis, Glass-Seagall act, deregulation (Thatcher-Reagan era), subprimes, CDO, Lehman Brothers bankruptcy, bail out plans, reinforcement of financial regulation
  • Prudential regulation since the subprime crisis: what has been done, what is left to be done
  • Other reforms: accounting, market structures, (CMU, IFRS, EMIR)
  • From CVA to XVA : high-frequency trading, blockchains, cryptocurrencies, negative rates, multivalued rate curves,…

Evaluation : written examination (QCM).

Acquired skills : History of regulation through successive crisis, and  its  impact on the design, the trading and the hedging of derivative products.

High Frequency and Algorithmic Trading

Course and small classes

Charles Albert Lehalle, Senior Researcher, CFM, Mathieu Rosenbaum, PR.        Ecole Polytechnique

Aim : Introduction to cutting edge statistical and stochastic control techniques for high frequency finance under the new regulatory environment.

Content :

  • Market microstructure after MIFID II
  • Introduction to high frequency modelling
  • High frequency statistics
  • Limit order book modelling
  • Optimal high frequency trading
  • Microstructure and volatility
  • Regulatory issues

Evaluation : written examination + project (joint with other courses).

Acquired skills : Master the principles, models and techniques of High Frequency and Algorithmic Trading in connection with the evolution of the regulation.

Energy Markets

Small classes

Olivier Bardou ENGIE & Sorbonne Université,   René Aïd, PR Dauphine

AIM : Introduction to the specificities of energy markets and to the mathematical tools.

Content :

  • Modeling of energy markets (gas, oil, electricity) : spcificities and mathematical tools. (stochastci convolutions, jump diffusions)
  • Dynamics of the underlying: spot prices , forward price structure, correlations,
  • Derivative contracts (swing option, sparks options, real options)
  • More about gas (gas plants, storage, take-or-pay contracts)
  • More about electricity (peaks, negative prices, etc)
  • Stochastic control methods for pricing energy derivatives : theoreticaal and numerical apsects.

Evaluation : written examination.

Acquired skills : Master the principle of modelling of assets and the pricing of spot/forward contracts on energy markets (especially gas and electricity).

Fintech/Retail finance

Small classes

Sébastien Choukroun, PwC

AIM : Basic notions of machine learning.

Content :

  • Introduction to cryptography
  • Tokenisation of asset by blockchain, bitcoin
  • Blockchain by ethereal, smart contracts
  • Ledger (securisation of crypto-currency)
  • Examples of use case

Evaluation : analysis of a use case.

Acquired skills : Understand the basics of blockchain technology and how to use it for crypto-currencies with a focus on use case.  

Machine learning

Course and small classes

Stéphane Gaiffas, PR. Ecole polytechnique

AIM : Basic notions of machine learning.

Content :

  • Supervised and unsupervised learning
  • Regression, classification
  • Recommendation and e-marketing
  • Tools for convex optimization, online stochastic optimization

Evaluation : written examination and/or project (shared with other courses).

Acquired skills : Master the basics from supervised and unsupervised in order to use the main plateforms recently released like tensorflow, pytorch, etc, in view of financial application.