Financial Mathematics

Course: Financial Mathematics

Code: 29016-AUX

Introduction:

Financial mathematics is a branch of applied mathematics that focuses on the mathematical tools used in the fields of finance and investment. This course will teach students how to apply mathematical concepts to analyze and evaluate financial instruments, manage risks, and apply stochastic processes in finance.

Objectives:

By the end of the course, students will be able to:

1. Understand and analyze the time value of money using simple and compound interest.

2. Price financial instruments such as stocks, bonds, and financial options.

3. Manage financial risks using models such as Value at Risk (VaR) and hedging techniques.

4. Understand and apply stochastic processes in finance such as Brownian motion and the Black-Scholes equation.

Main Topics:

1. Time Value of Money:

   • Simple and Compound Interest: Understanding how to calculate interest on loans or investments using both simple and compound interest methods.

   • Amortization Tables: How to calculate monthly payments for loans or installments using financial tables.

2. Pricing Financial Instruments:

   • Stocks and Bonds: Analyzing how to price stocks and bonds based on returns and market variables.

   • Financial Options: Understanding how to price financial options using models like the Black-Scholes model.

3. Risk Management:

   • Value at Risk (VaR) Models: Learn how to measure financial risk using the Value at Risk (VaR) model and interpret these values.

   • Financial Hedging: Hedging strategies using financial instruments such as options and futures to mitigate risk.

4. Stochastic Processes in Finance:

   • Brownian Motion: Understanding the stochastic process of Brownian motion and its application in financial markets.

   • Black-Scholes Equation: Learning how to use the Black-Scholes equation to price financial options and its applications in the market.

Duration:

• Course Duration: 10 weeks

• Sessions: 2 lectures per week (90 minutes per lecture)

Level:

• Level: Advanced

• Prerequisites: Basic knowledge of financial mathematics, calculus, and linear algebra.

Learning Materials:

• Textbooks:

  • “Financial Mathematics: A Comprehensive Treatment” by Giuseppe Campolieti, Roman N. Makarov

  • “Options, Futures, and Other Derivatives” by John C. Hull

• Software:

  • Excel (for financial analysis and table setup)

  • MATLAB or Python (for solving financial equations and applying models)

Teaching Methods:

• Theoretical Lectures: Detailed explanation of mathematical tools and financial models.

• Practical Exercises: Hands-on exercises on financial calculations, option pricing, and Black-Scholes applications.

• Projects and Case Studies: Real-world financial market or company case studies for analysis.

Course Schedule:

Assessment:

• Assignments: 30% of final grade (weekly practical exercises)

• Midterm Exam: 30% of final grade (covering time value of money and pricing financial instruments)

• Final Exam: 40% of final grade (covering all topics covered in the course)

Final Goal:

By the end of the course, students will have the ability to analyze financial instruments using mathematics, price financial options using the Black-Scholes equation, and manage financial risks with models like VaR. They will possess the necessary skills to make informed financial decisions based on mathematical models in finance.

This course equips students with the key mathematical tools used in financial markets, preparing them for careers in financial analysis, investment banking, or quantitative finance.