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2024/2025  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 25-01-2024

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, jumps, and local volatility
  • Derive the characteristic function of log prices in settings with stochastic volatility and jumps; discuss and implement the pricing of European put and call options by Fourier inversion techniques
  • Design efficient simulation schemes for pricing options with path-dependent payoffs and early exercise features
  • Explain the decomposition of various structured products into their underlying option components
  • Understand the model risk associated with pricing and hedging exotic derivatives and structured products
  • Design and value various corporate debt securities
  • Demonstrate the model-independent pricing of variance swaps; explain empirical results on the volatility risk premium
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 is an emphasis on implementation of models and numerical methods and we will use Python and Excel, although students can use other software. The final exam will be structured so that it can be solved using Excel only. While the course is targeted towards cand.merc.mat students, all students with the necessary prerequisites are welcome. In previous years, students from "Advanced Economics and Finance" and "Finance and Investments" as well as students from KU and DTU have attended.
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 consists of three parts: The first part covers the type of pricing models that institutions use for valuation and risk management of derivatives. We consider models with stochastic volatility, jumps, and local volatility such as the Heston, Merton, Kou, Bates, Dupire, and SABR models. We also cover how to calibrate these models to volatility surfaces using mostly Fourier inversion techniques. The second part of the course shows how to use simulation to price more complicated derivatives with path-dependent and early-exercise features including the Longstaff-Schwartz LSM method. The third part of the course then shows how to engineer a wide variety of structured products (e.g., capital protection notes, yield enhancement notes, cliquets, reverse cliquets), corporate debt securities (e.g., callable bonds, convertible bonds), volatility derivatives (e.g., variance swaps) etc. The models and methods covered in 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
Most weeks I will post assignments that we then solve together in class where students can ask questions and get feedback. These assignments are not mandatory. However, most are highly exam-relevant so it is strongly recommended that students try to solve them in order to get maximum feedback and prepare for the final exam.

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 25-01-2024