This lecture discusses the basic mathematical tools for continuous-time finance and applies these to problems in derivative pricing. In particular we study option pricing in the Black Scholes model.
We will cover the following topics
- Wiener process and compound Poisson processes
- Quadratic variation
- Pathwise Ito calculus, elementary Ito integral and the Ito formula
- Generators and Feynman Kac for one-dimensional diffusions
- Derivative pricing via replication in the Black Scholes model
- Black Scholes formula and application
- Extensions beyond the classical Black Scholes model
- Basic numeric approaches for option pricing
Continuous time finance is concerned with: Brownian motion, stochastic calculus, risk-neutral pricing, stochastic and partial differential equations, exotic options.
After completing this class the student will have the ability to:
• describe the basic concepts and methods of continuous time finance;
• apply and do computational work with the basic concepts and definitions of continuous time finance.
After completing this class the student will also have the ability to:
• confidently apply ideas of continuous time finance in doing analytical work for financial markets.
• solve applied problems where skills are required from continuous time finance.
Standard rules for PIs (80 % of lectures and tutorium)
This class is taught as a lecture complemented with exercises and a tutorium
Midterm Exam (20%)
Exercise Series (25%)
Final exam (55%)
A minimum score of 40% in the final exam and an overall score of 50 % is necessary for passing.
Exercises will be discussed during the tutorium (also additional exercises).
• Advanced Business Mathematics (class Mathematics I of the QFin program);
• Advanced Business Probability theory (class Probability of the QFin program);
Probability and Mathematics II from QFin or equivalent