The Fundamentals of Quantitative Finance

The "Fundamentals of Quantitative Finance" training program is structured to provide a rigorous introduction to the mathematical concepts and analytical tools essential for financial market modeling.

Designed for professionals such as analysts, traders, and risk managers, this course covers key concepts:

• Stochastic calculus and asset price dynamics
• Option pricing: Black-Scholes-Merton model and extensions
• Interest rate models: Vasicek, Cox-Ingersoll-Ross

Combining theory (probability, stochastic differential equations, risk-neutral measures) and practice (simulations, model calibration), this course enables participants to:

• Master the mathematical formalization of financial problems
• Implement pricing methods and risk management strategies
• Analyze and interpret quantitative models in a professional context

This course provides an essential foundation for professionals seeking to apply quantitative tools in finance.

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The Fundamentals of Quantitative Finance

I. Introduction and Fundamentals

• Definition of Quantitative Finance: Understanding its objectives and applications in financial markets.
• The Different Profiles of “Quants”: Trading, risk management, quantitative research, and algorithm development.
• Essential Mathematical Concepts:
  • Differential and integral calculus: foundations and applications in finance.
  • Linear algebra: matrices, determinants, and eigenvectors.
  • Probability: fundamental laws, conditional expectation, and independence.
  • Statistics: regressions, hypothesis testing, and parameter estimation.

Practical Case Study:

Solving a system of equations to determine the expected return of 3 distinct assets.

II. Introduction to Stochastic Calculus

• Symmetric Random Walk, Brownian Motion, Stochastic Processes, and Itô’s Lemma: Understanding the basics of continuous random processes.
• Black-Scholes Model and Binomial Tree:
  • Explanation of the assumptions and the Black-Scholes formula.
  • Methodology of binomial trees for option pricing.

Practical Case Study:

• Using Itô’s Lemma to solve the Black-Scholes partial differential equation.
• Building a binomial tree to evaluate a European option.

III. Interest Rate Models

• Vasicek Model – Application to bond markets and rate forecasting.
• Cox-Ingersoll-Ross (CIR) Model – Rate evolution under variable volatility.
• Hull-White Model – Incorporating deterministic terms into interest rate models.
• Heath-Jarrow-Morton (HJM) Model – Comprehensive modeling of the yield curve.
• Libor Market Model (LMM) – Applications in pricing interest rate derivatives.

Practical Case Study:

Using the Vasicek model to estimate interest rate evolution.

IV. Risk Management

• Risk Measurement and Management: Identification of different risk types (market, credit, counterparty, liquidity).
• Value at Risk (VaR) and Conditional VaR (CVaR): Tools for measuring potential extreme losses.
• Stress Testing and Scenario Analysis: Anticipating and simulating extreme shocks in financial markets.

Practical Case Study:

Calculating VaR and CVaR.

V. Portfolio Management

• Efficient Frontier and Capital Allocation Line – Foundations of modern portfolio theory.
• Sharpe Ratio and Optimization – Maximizing risk-adjusted returns.
• Capital Asset Pricing Model (CAPM) and Multi-Factor Models – Explanation and implementation of asset valuation models.
• Mean-Variance Optimization (MVO) and Black-Litterman Model – Traditional and advanced approaches to portfolio optimization.
• Introduction to “Entropy Pooling.”

Practical Case Study:

Building a portfolio of assets using various models.

VI. Pricing and Valuation

• Exotic Options:
  • Understanding complex options and their volatility.
  • Developing tailored hedging strategies.
• Pricing Exotic Options:
  • Analytical models: binomial trees, Black-Scholes.
  • Numerical models: Monte Carlo, finite differences.
• Pricing and Valuing Credit Derivatives:
  • Introduction to correlation, dependence structures, and marginal distributions.
  • Copula models, CDOs, and “first to default.”
  • Techniques for extreme risk hedging.

Practical Case Study:

Using Excel-based pricers with copula models.