This is a series of introductory courses in quantitative finance, providing a practical understanding of the intuition behind the formulas.
1. Introduction to quantitative finance :
In this introduction to quantitative finance, I will present the crucial role it plays in understanding financial markets and managing risk.
2. Stochastic processes:
We'll explore the concept of stochastic processes, showing how they represent random processes evolving over time. Asset prices are often modeled in this way because of their unpredictable nature.
3. Stochastic calculus :
In this section, we'll dive into stochastic calculus as the branch of mathematics used to study random-walk processes. You'll see how it enables us to model and analyze complex financial processes that structurally involve uncertainty.
4. Brownian motion :
I'll introduce you to Brownian motion, an essential stochastic process widely used in finance to model asset price movements.
You'll understand that this model is based on the assumption that price variations are unpredictable and that there are no trends or directional biases associated with these variations.
5. Itô's Lemma :
Itô's lemma is an essential concept in finance, and I'll explain it to you simply.
You'll understand its importance, as it allows you to find the rate of change of stochastic process functions.
Itô's Lemma is an important mathematical result used in quantitative finance and the analysis of stochastic processes. It is widely used to study the evolution of random variables such as the price of financial assets.
It therefore plays an essential role in the analysis of financial derivatives and in the modeling of random fluctuations in financial assets.
6. Option valuation :
We'll look at the concept of option pricing and its importance in financial markets. You'll see that stochastic calculus is used in the Black-Scholes model, which is fundamental to the valuation of conditional derivatives such as options.
7. Risk management :
In this section, I'll show you how stochastic calculus specifically contributes to risk management by quantifying market risks and identifying appropriate hedging strategies.
You'll also understand how it is used to estimate potential losses in financial portfolios.
8. Monte Carlo simulation :
Monte Carlo simulation is a fundamental numerical method in quantitative finance.
I'll explain how it can be used to approximate solutions to complex problems.
This approach involves generating random scenarios to model uncertainty in the behavior and evolution of any asset, especially financial assets.
Detailed program of “Quantitative finance made accessible…” courses I will conduct. This is an introductory webinar not “maths-oriented” but “intuition and practice-oriented”. More to come…
Course 1: Introduction to Quantitative Finance
1. Role of quantitative methods in finance
2. Importance of mathematical modeling
- Mini Case Study: Explore different “quant jobs” by analyzing financial career job offers on www.efinancialcareers.com and understanding the skills and responsibilities required in various quantitative roles.
Course 2: Stochastic Processes in Finance
1. Introduction to stochastic processes' role in modeling financial markets
2. Utilizing Brownian motion for modeling asset price movements
3. Linking Brownian motion to geometric Brownian motion and Black-Scholes model
- Mini Case Study: A derivatives trader uses geometric Brownian motion to price European call options and hedge against stock price fluctuations.
Course 3: Poisson Processes and Jump Diffusion
1. Incorporating Poisson processes to model rare events and jumps in prices
2. Applying jump diffusion models to capture extreme market movements
- Mini Case Study: An insurance company models the occurrence of large-scale catastrophic events using a Poisson process to estimate potential claims.
Course 4: Financial Modeling and Derivatives
1. Options and Option Pricing
- Black-Scholes model for option pricing
- Mini Case Study: A quant analyst values an exotic option with complex payoffs using a combination of the Black-Scholes model and Monte Carlo simulations.
Course 5: Interest Rate Modeling
1. Short-rate models (Vasicek, Cox-Ingersoll-Ross)
2. Term structure models (Yield curve, Heath-Jarrow-Morton framework)
- Mini Case Study: A fixed income strategist applies the Cox-Ingersoll-Ross model to forecast changes in interest rates and optimize bond portfolio returns.
Course 6: Risk Management and Portfolio Optimization
1. Risk Metrics and Measures
- Value at Risk (VaR) and Expected Shortfall (ES)
- Using risk measures for portfolio assessment
- Mini Case Study: A risk manager calculates Value at Risk to determine the potential loss of a portfolio due to adverse market conditions.
2. Portfolio Optimization
- Mean-variance optimization
- Modern portfolio theory and capital asset pricing model
- Mini Case Study: A wealth manager constructs a diversified investment portfolio that maximizes expected returns while minimizing overall risk.
Course 7: Quantitative Trading Strategies
1. Quantitative Trading Strategies
- Statistical arbitrage, pairs trading, and mean-reversion strategies
- Trend-following and momentum strategies
Mini Case Study: A hedge fund implements a pairs trading strategy to profit from price divergences between closely related stocks.
A zoom link will be sent to registered participants only the day before each course.
N.B: It will be a course explaining the intuition of practical financial models behind mathematics and not a course in "mathematics applied to finance". I will explain the concepts and the need for specific mathematical tools (without demonstrating or going into the details of formulas and other lemmas) to achieve practical goals, and in particular: pricing and valuation of financial instruments (cash and derivatives), risk management, portfolio optimization, financial engineering and hedging.
Dates and time:
First class: Saturday, September 30 (duration: 1 hour)
Second class: Saturday, October 6 (duration: 1 hour)
Third class: Saturday, October 13 (duration: 1 hour)
Fourth class: Saturday, October 20 (duration: 1 hour)
Fifth class: Saturday, October 27 (duration: 1 hour)
Sixth class: Saturday, November 4 (duration: 1 hour)
Seventh class: Saturday, November 11 (duration: 1hour)
Each class will take place at 3:00 PM UTC/GMT +2 hour