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2023/2024  KAN-CMECV1251U  Financial Engineering

English Title
Financial Engineering

Course information

Language English
Course ECTS 7.5 ECTS
Type Elective
Level Full Degree Master
Duration One Semester
Start time of the course Autumn
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
  • Anders Bjerre Trolle - Department of Finance (FI)
Main academic disciplines
  • Finance
Teaching methods
  • Face-to-face teaching
Last updated on 13-02-2023

Relevant links

Learning objectives
At the end of this course, the student should be able to:
  • Describe properties of asset returns and implied volatility surfaces
  • Compare and contrast different methods for modeling implied volatility surfaces including stochastic volatility, local volatility, and jumps
  • Derive the characteristic function of log stock prices in settings with stochastic volatility and jumps; discuss and implement the pricing of European put and call options by Fourier inversion techniques
  • Implement an implied binomial tree
  • Design efficient simulation schemes for pricing options with path-dependent payoffs and early exercise features
  • Explain the decomposition of structured products into their underlying option components
  • Understand the model risk associated with pricing and hedging exotic derivatives and structured products
  • Demonstrate the model-independent pricing of variance swaps; explain empirical results about volatility risk premiums
Course prerequisites
Students must have taken a basic derivatives course and be familiar with the Black-Scholes model and binomial trees. Students must also have basic knowledge of stochastic differential equations and Ito's Lemma. There will be an emphasis on implementation of models and numerical methods; therefore, the course requires familiarity with a software package that can be used for numerical computation. It will, however, be possible to solve the exam using Excel. While the course is targeted towards cand.merc.mat students, all students with the necessary prerequisites can follow the course.
Prerequisites for registering for the exam (activities during the teaching period)
Number of compulsory activities which must be approved (see section 13 of the Programme Regulations): 1
Compulsory home assignments
There will be one mandatory assignment that is graded as failed/passed. The assignment can be done in groups of up to four students
Financial Engineering:
Exam ECTS 7,5
Examination form Written sit-in exam on CBS' computers
Individual or group exam Individual exam
Assignment type Written assignment
Duration 3 hours
Grading scale 7-point grading scale
Examiner(s) One internal examiner
Exam period Autumn
Aids Limited aids, see the list below:
The student is allowed to bring
  • An approved calculator. Only the models HP10bll+ or Texas BA ll Plus are allowed (both models are non-programmable, financial calculators).
  • Language dictionaries in paper format
The student will have access to
  • Advanced IT application package
Make-up exam/re-exam
Same examination form as the ordinary exam
The number of registered candidates for the make-up examination/re-take examination may warrant that it most appropriately be held as an oral examination. The programme office will inform the students if the make-up examination/re-take examination instead is held as an oral examination including a second examiner or external examiner.
Course content, structure and pedagogical approach

The course covers important topics within financial engineering. The course consists of three parts: The first part covers the type of pricing models that institutions use for risk management and valuation of stuctured products and exotic derivatives. We consider models with local volatility, stochastic volatility, and jumps. We also cover how to calibrate these models to standard put and call options using Fourier inversion techniques. The second part of the course covers numerical techniques (primarily simulation) used for pricing more complicated derivatives with path-dependent and early-exercise features. The third part of the course covers a range of applications. The models and methods covered by the course have wide applications across equity, fixed income, credit, FX, and commodity/energy markets.

Description of the teaching methods
Feedback during the teaching period
For most lectures, I will post an exam-relevant assignment beforehand that we go through together at the beginning of the lecture, where students can ask questions and get feedback. These assignments are not mandatory, but it is very highly recommended that students solve them in order to get maximum feedback.

There will be regular office hours throughout the semester.
Student workload
Lectures 32 hours
Preparations 128 hours
Mandatory assignment 16 hours
Final exam (including preparation) 30 hours
Expected literature

Required readings are slides and lecture notes.


The following textbooks cover many of the topics in the course, but are not required readings:

- Gatheral, “The Volatility Surface", Wiley, 2006

- Rouah, "The Heston Model", Wiley, 2013


Useful background on derivatives pricing can be found in (among others)

- Sundaram and Das, “Derivatives”, McGraw-Hill, 2016 (second edition)

- Kosowski and Neftci, “Principles of Financial Engineering”, Academic Press, 2015


Last updated on 13-02-2023