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Financial Mathematics with Julia

Financial Mathematics with Julia

Financial Risk Management with Julia: A Detailed Syllabus

Course Description: This course provides a comprehensive introduction to financial risk management, combining theoretical foundations with practical applications using the Julia programming language. Students will learn about various types of financial risk, quantitative methods for risk assessment, and techniques for risk mitigation. The course emphasizes hands-on experience through coding exercises, case studies, and a final project.

Prerequisites:

  • Basic programming knowledge (preferably in any language, Julia experience is a plus but not required).
  • Familiarity with basic statistical concepts (probability, distributions, etc.).
  • Basic understanding of financial markets and instruments (stocks, bonds, derivatives).

Course Objectives: Upon completion of this course, students will be able to:

  • Understand the fundamental concepts of financial risk management.
  • Identify and classify different types of financial risk (market, credit, operational, liquidity).
  • Apply quantitative methods for risk measurement (VaR, Expected Shortfall, stress testing).
  • Implement risk management techniques using the Julia programming language.
  • Use Julia packages for financial modeling, statistical analysis, and optimization.
  • Analyze case studies of real-world risk management challenges.
  • Develop a risk management project using Julia.

Course Structure:

The course will consist of lectures, hands-on coding sessions, guest lectures from industry professionals (where possible), and a final project.

Modules:

Module 1: Introduction to Financial Risk Management (2 weeks)

  • What is financial risk?
  • Types of financial risk: market risk, credit risk, operational risk, liquidity risk.
  • The role of risk management in financial institutions.
  • Risk management frameworks and regulations.
  • Introduction to Julia for financial applications.
    • Setting up Julia and necessary packages (e.g., DataFrames.jl, Distributions.jl, StatsPlots.jl, FinancialMonteCarlo.jl, JuMP.jl).
    • Basic Julia syntax and data structures.
    • Working with financial data in Julia.

Module 2: Market Risk (4 weeks)

  • Value-at-Risk (VaR): historical simulation, Monte Carlo simulation, parametric VaR.
  • Expected Shortfall (ES).
  • Stress testing and scenario analysis.
  • Backtesting VaR models.
  • Volatility modeling (GARCH models).
  • Implementing market risk models in Julia.
    • Simulating asset price paths using Monte Carlo methods.
    • Calculating VaR and ES using different methods.
    • Implementing backtesting procedures.
    • Estimating GARCH models using Julia packages.

Module 3: Credit Risk (4 weeks)

  • Credit risk assessment: probability of default, loss given default, exposure at default.
  • Credit scoring and rating.
  • Credit portfolio management.
  • Credit derivatives (CDOs, CDS).
  • Modeling credit risk in Julia.
    • Simulating credit defaults using copula models.
    • Calculating credit portfolio loss distributions.
    • Pricing credit derivatives.

Module 4: Operational Risk (3 weeks)

  • Identifying and measuring operational risk.
  • Qualitative and quantitative methods for operational risk assessment.
  • Basel II/III framework for operational risk.
  • Implementing operational risk models in Julia (e.g., frequency-severity models).

Module 5: Liquidity Risk (2 weeks)

  • Types of liquidity risk: market liquidity risk, funding liquidity risk.
  • Measuring and managing liquidity risk.
  • Liquidity risk stress testing.
  • Modeling liquidity risk in Julia.

Module 6: Risk Management Frameworks and Regulations (2 weeks)

  • Basel Accords (Basel I, II, III).
  • Solvency II.
  • Enterprise Risk Management (ERM).
  • Regulatory reporting and compliance.

Module 7: Advanced Topics (2 weeks)

  • Model risk.
  • Climate risk.
  • Fintech and risk management.
  • Ethical considerations in risk management.

Assessment:

  • Homework assignments (30%)
  • Midterm exam (30%)
  • Final project (40%)

Final Project:

Students will work on a risk management project using Julia. Project topics can include:

  • Developing a market risk model for a specific portfolio.
  • Building a credit risk model for a portfolio of loans.
  • Implementing an operational risk management framework.
  • Designing a stress testing scenario for a financial institution.
  • Analyzing the impact of climate change on financial risk.

Software:

  • Julia (latest version)
  • Relevant Julia packages (e.g., DataFrames.jl, Distributions.jl, StatsPlots.jl, FinancialMonteCarlo.jl, JuMP.jl, QuantLib.jl, FixedIncome.jl)

Recommended Textbooks:

  • Risk Management and Financial Institutions by John C. Hull
  • Financial Risk Management: A Practical Guide by Stephen Allen
  • Julia Programming for Data Science by Zachary del Rosa and Andreas Noack

Julia Resources:

This syllabus provides a structured approach to learning financial risk management with a strong emphasis on practical application using the Julia programming language. The combination of theoretical knowledge, hands-on coding experience, and a real-world project will equip students with the skills necessary to succeed in the field of financial risk management.