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Engineering Cycle – Major in Quantitative Finance

Illustrative image of the Finance specialization of the ECE Engineers program
  • Calculation of probability distributions for gains and losses in financial markets.

  • Pricing and coverage of derivative instruments: options, swaps, and exotic products.

  • Stochastic simulation techniques: Monte Carlo, finite difference methods.

  • Large-Scale Market Dynamics: Analogies with Statistical Physics and Thermodynamics.

  • Application of machine learning and AI to asset management and market forecasting.

  • Quantitative management of market, credit, and liquidity risks.

    Content

    The courses combine traditional training in quantitative finance with new digital approaches. Redesigned for digital finance, they preserve the strengths of mathematics while integrating tools from AI and data science. They evolve each year to align with industry advancements.

    60 ECTS credits/year

    Stochastic Calculus and Advanced Mathematics

    • Itô stochastic calculus and stochastic differential equations
    • Multivariable analysis and variational calculus applied to markets
    • Advanced probabilities: Wiener processes, martingales, risk-neutral measures
    • Numerical simulation methods: Monte Carlo, quasi-Monte Carlo

    Pricing and derivative instruments

    • Black-Scholes model and extensions: Heston, SABR, jump models
    • Option pricing: European, American, exotic
    • Interest rate products: swaps, caps, floors, swaptions

    Model calibration to market data

    • Quantitative finance and markets
    • Financial markets as physical systems: thermodynamic analogy
    • Large-scale markets: many agents and probability distributions
    • Introduction to algorithmic trading and high frequency
    • Quantitative technical and fundamental analysis

    Computing and data for finance

    • Python for quantitative finance: NumPy, SciPy, QuantLib
    • Financial databases and market data processing
    • Introduction to machine learning applied to finance
    • Team Multidisciplinary Project (PPE)

    Internship – minimum 3 months in a financial institution or quantitative desk

    90 ECTS credits/year


    Advanced Market Modeling

    • Local and stochastic volatility models: Dupire, Heston, hybrid models
    • Modeling of equity, interest rate, credit, and commodity markets
    • Jump models and Lévy processes
    • Market finance and analogies with fluid mechanics

    Quantitative Risk Management

    • Value at Risk (VaR), Expected Shortfall, and coherent risk measures
    • Credit risk: structural and reduced-form models, CVA/DVA
    • Liquidity risk and market risk under Basel IV
    • Stress testing and quantitative crisis scenarios

    Machine Learning and AI for Financial Markets

    • Deep learning for forecasting and pricing financial instruments
    • Reinforcement learning applied to algorithmic trading
    • NLP for market sentiment analysis and news processing
    • Generative AI and language models applied to finance

    Cryptocurrencies and Alternative Finance

    • Strategic foresight around cryptocurrencies (ECE research lab)
    • Economic models and dynamics of crypto asset markets
    • Decentralized finance (DeFi) and blockchain protocols

    Minor and specialization

    • Minor of choice: transversal to technologies
    • Specialization option: growth sector or cutting-edge expertise
    • Value Creation of Student Projects (VPE) – IDEFI program
    • Final Year Project (PFE)

    Internship as an engineer – minimum 6 months in banking, quantitative desk, or fund

    Mandatory international semester (4th or 5th year)

    Evaluation methods

    • Stochastic modeling projects based on real market data.
    • Pricing and hedging work for derivatives in Python or C++.
    • The Multidisciplinary Team Project (PPE) and the End of Studies Project (PFE).
    • A minimum 6-month engineering internship in quantitative desk or financial institution, with a report and defense.
    • An obligatory international semester, validated with a partner university of ECE.

    Certified by the state

    Validated skills

    Prepares for employment

    • A minimum 3-month internship during the 4th year, in a trading desk, an investment fund, or a financial institution.

    • An engineering internship of at least 6 months during the 5th year of study, culminating in a final project defended before a panel.

    • A mandatory international semester at one of the ECE's 160 academic partner institutions.

    • Research projects in collaboration with the ECE's partner laboratory, which specializes in macroeconomic models and crypto-assets.

      Étudiante du programme Ingénieurs de l’école d’ingénieurs ECE se tenant fièrement face caméra, habillée en tenue professionnelle
      • Portrait photo of Nathan Orsinet

        A big thank you to ECE for its support throughout my academic career! My specialization in Finance allowed me to combine my engineering skills with quantitative analysis, data, and financial issues. This dual approach is now very useful to me as I explore new topics, particularly those related to automation and artificial intelligence as applied to finance.

        Nathan OrsinetDéveloppeur Visual Basic
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