2024/2025 KANCMECV1250U Mathematical Finance 2: Continuous Time Finance
English Title  
Mathematical Finance 2: Continuous Time Finance 
Course information 

Language  English 
Course ECTS  7.5 ECTS 
Type  Elective 
Level  Full Degree Master 
Duration  One Quarter 
Start time of the course  Second Quarter 
Timetable  Course schedule will be posted at calendar.cbs.dk 
Max. participants  80 
Study board 
Study Board for HA/cand.merc. i erhvervsøkonomi og matematik,
MSc

Course coordinator  


Main academic disciplines  


Teaching methods  


Last updated on 13032024 
Relevant links 
Learning objectives  
By the end of the course, students will be
confident with the probabilistic techniques required to understand
the most widely used models in finance, from the BlackScholes
model to stochastic volatility models and affine term structure
models.
To achieve the grade 12, students should meet the following learning objectives with no or only minor mistakes or errors:


Course prerequisites  
Prerequisites equivalent to the level of the HA(mat.) program. Particularly, students must have taken a basic derivatives course. It is an advantage to have followed Matematisk Finansiering 1 but it is not a prerequisite. Undergraduate knowledge of probability theory, algebra and calculus is required.  
Examination  


Course content, structure and pedagogical approach  
Over the last few decades, financial analysts have started using more and more sophisticated mathematical concepts and models to describe the behaviour of markets and to derive computing methods. This course provides an introduction to stochastic calculus and shows how it is applied to the pricing and hedging of financial contracts such as equity options and interest rate derivatives. The goal is to make students confident with the probabilistic techniques required to understand the most widely used financial models. The course is mainly suitable for students who would like to become quantitative analysts, asset managers, traders, risk managers, structurers, or who are simply generally interested in financial markets and want to gain the technical skills needed to understand and model their behaviour.
The course is split into 4 sections:
1. Discrete Time Finance: the Binomial Model
2. Introduction to Stochastic Processes and Stochastic Calculus
3. Pricing and Hedging in Continuous Time
4. Advanced material (time permitting)


Description of the teaching methods  
The lectures will include exercise sessions where
the students have (limited) time to work on problem sets that will
then be discussed afterwards.
The pedagogical approach of the course is applied in nature. That means that we will abstract from much of the (deep) technical rigour underlying continuous time theory and instead concentrate on applications and problem solving. In other words, we will be ‘learningbydoing’, which will require investing time in problem sets and exercises. We will also discuss few programming exercises to illustrate the how the theoretical models taught in the course are implemented in practice. 

Feedback during the teaching period  
The students are encouraged to actively
participate in the lectures and problemsolving sessions.
Exercise sets will be regularly distributed and selected problems solved in class. Solutions will be provided. There will be feedback during the problemsolving sessions and the students can compare their own exercise solutions with the lecturer's solutions and students can receive hints and comments on their proposed solutions. The course will also incorporate blended learning, where a portion of the feedback will take place online. 

Student workload  


Further Information  
The course can be taken by any interested student


Expected literature  
The main textbook is: ``Arbitrage Theory in Continuous Time'', Björk (2020)
Selected chapters from the following textbooks will also be covered: ``Stochastic Calculus for Finance: Discretetime Models'', (2004) Shreve ``Stochastic Calculus for Finance II: Continuoustime Models'' , (2004) Shreve
(all books are available online through CBS library)
