Computational Finance

Owner	Master Computational Science (joint degree)
Coordinator	dr. Sven Karbach
Part of	Master Computational Science (Joint Degree), Master Stochastics and Financial Mathematics, specialization Data Analysis and Statistics, year 1Master Stochastics and Financial Mathematics, specialization Financial Mathematics, year 1Master Stochastics and Financial Mathematics, specialisation Probability and Decision Making, year 1
Links	Visible Learning Trajectories

Course manual 2025/2026

Course content

This course provides a rigorous introduction to modern computational methods for the pricing and hedging of derivative securities. Students develop a deep understanding of volatility, including historical, implied, and stochastic volatility, and its central role in financial markets. Starting from the principles of arbitrage-free pricing and the Black-Scholes framework, the course progresses to advanced derivative products and numerical techniques.

Core topics include risk-neutral valuation, stochastic differential equation (SDE) modeling of asset dynamics and volatility, Monte Carlo simulation, partial differential equation (PDE) methods for option pricing, and the calibration of financial models to market data. Students also learn the computation and interpretation of Greeks for risk management and hedging.

The course emphasizes both mathematical foundations and practical implementation, equipping students with computational tools widely used in modern quantitative finance and financial engineering.

Study materials

Other

• Lecture Notes

   

Objectives

• Understand foundational theories in financial pricing, risk modeling, and stochastic processes.
• Implement numerical methods (e.g., Monte Carlo simulations, PDE solvers) using Python.
• Model and calibrate financial instruments.
• Develop computational solutions for pricing derivatives and managing risk.
• Critically evaluate simulation results and effectively communicate technical findings.
• Collaborate on practical projects and independently solve complex financial problems.

Teaching methods

• Lecture
• Computer lab session/practical training

The course emphasizes knowledge transfer and practical guidance, with lectures focusing on core principles and computational methods. Practitioner sessions, led by industry experts, complement the theoretical content by addressing real-world problems in computational finance.

Through hands-on coding exercises and group projects, students will develop robust problem-solving skills and technical proficiency. The course also introduces industry-standard tools in Python, fostering practical expertise applicable to various domains in quantitative finance.

Learning activities

Attendance

This programme does not have requirements concerning attendance (Ter part B).

Assessment

Item and weight	Details
Final grade
1 (100%) Tentamen

Assignments

[{"Item1":"Project 1","Item2":"

First Lab Exercise and Homeowk (group, feedback on assignment, graded)

"},{"Item1":"Project 2","Item2":"

Second Lab Exercise and Homeowk (group, feedback on assignment, graded)

"},{"Item1":"Project 3","Item2":"

Third Lab Exercise and Homeowk (group, feedback on assignment, graded)

"},{"Item1":"Exam","Item2":"

Written Exam (individual, feedback on exam, graded)

"}]

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Additional information

Recommended prior knowledge: Basic programming skills and mathematics (calculus and probability theory).

Contact information

Coordinator

• dr. Sven Karbach