◉ Current Context

In an increasingly complex and regulated financial environment, this training addresses the growing needs of professionals in:

• Advanced modeling of financial instruments
• Accurate valuation of derivative products
• Quantitative market risk management

• Master fundamental mathematical concepts
• Understand the Black-Scholes model and its extensions
• Apply option pricing methods

• Analyze main interest rate models
• Implement risk management strategies
• Solve concrete financial modeling cases

◉ Available in-person and remotely ◉ Training materials provided ◉ Training certificate

I. Introduction and Foundations

• Definition of Quantitative Finance: Understanding its objectives and applications in financial markets.
• Different "Quant" Profiles: Trading, risk management, quantitative research, and algorithm development.
• Essential Mathematical Concepts:
  • Differential and integral calculus: fundamentals and financial applications.
  • Linear algebra: matrices, determinants, and eigenvectors.
  • Probability: fundamental distributions, 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

• 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 assumptions and the Black-Scholes formula.
  • Binomial tree methodology 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 in interest rate models.
• Heath-Jarrow-Morton (HJM) Model - Complete yield curve modeling.
• Libor Market Model (LMM) - Applications in interest rate derivative pricing.

Practical Case Study:

Using the Vasicek model to estimate interest rate evolution.

IV. Risk Management

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

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 pricing models.
• Mean-Variance Optimization (MVO) and Black-Litterman Model - Traditional and advanced portfolio optimization approaches.
• Introduction to Entropy Pooling.

Practical Case Study:

Building an asset portfolio using different models.

VI. Valuation and Pricing

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

Practical Case Study:

Using Excel-based pricers with copula models.