AØKK08370U  Derivative Pricing (F)

Volume 2017/2018

MSc programme in Economics – elective course

The course is part of the MSc programme in Economics-Financial line (symbolized by ‘F’).



The course will give the student a solid foundation in both classical and modern aspects of option pricing and trading. We will start out by developing a thorough understanding of the notion of replication. Following this, we cover the famous Black-Scholes (1973) model which is the backbone of option pricing in practice still today. We then look at the model’s shortcomings and the presence of the so-called implied volatility smile. The volatility smile has been a main driver for the theoretical development in option pricing we have experienced over the past 30 years. We will look at modern extensions, e.g., stochastic volatility models, which have been proposed to address the vol smile. While option pricing theory is necessarily quite mathematical, the course will also try to develop the student’s intuitive understanding of the results. Furthermore, the course will consider several practical examples and assignments from especially fixed income, giving the student a feeling of how the theory comes to life on the trading floor.


A tentative list of topics that may be covered in the course:

  • Static and Dynamic Replication
  • The Black-Scholes Model
  • Options Hedging
  • The Volatility Smile
  • Trading Strategies
  • Local Volatility Models
  • Stochastic Volatility Models
  • Some Numerical Methods
  • Jump-Diffusion Models
Learning Outcome

After completing the course, the student should be able to:


  • Describe and understand common options and the mechanics underlying them

  • Explain the terminology used in the industry

  • Explain the motivation behind different options and their use.

  • Explain the motivation behind different pricing models and their use.

  • Discuss hedging strategies

  • Discuss trading strategies

  • Discuss option pricing models

  • Discuss numerical methods for pricing models



  • Calculate prices and quantify risk figures for common options using various models

  • Calibrate different pricing models to market data.

  • Evaluate the advantages and disadvantages of pricing models

  • Evaluate advantages and disadvantages of hedging strategies

  • Evaluate advantages and disadvanteages of trading strategies

  • Analyze option trades

  • Analyze hedging strategies

  • Analyze pricing models



  • Formulate and structure risks in terms of options/derivatives

  • Formulate and struture option pricing models

  • Develop and implement hedging strategies

  • Develop and implement trading strategies

  • Combine the theory of option pricing and empirical/practical implementation

The main reference is E.Derman & M.B. Miller, “The Volatility Smile” (2016). However, the course will also include various research papers.

The course is not intended to be an introductory course. Students are assumed to have prior knowledge of fixed income markets (mainly Bonds and Swaps) and basic contingent claim theory (e.g. from “Corporate Finance and Incentives” or “Pricing Financial Assets ”) at the level of the Hull textbook ("Options, futures, and other derivatives"). Finally, as the course is quite quantitatively demanding, students should at least have some interest in math and statistics.
Lectures, tutorials, and discussions of research papers
2 hours lectures 1 to 2 times a week from week 6 to 20 (except holidays).

The overall schema for the Master can be seen at

Timetable and venue:
To see the time and location of lectures please press the link/links under "Se skema" (See schedule) at the right side of this page (E means Autumn, F means Spring).

You can find the similar information partly in English at
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-F18; [Name of course]”
-Select Report Type: “List – Weekdays”
-Select Period: “Forår/Spring – Week 5-30”
Press: “ View Timetable”
7,5 ECTS
Type of assessment
Written examination, 3 hours under invigilation
at the computers of the university. The exam assignment is given in English and must be answered in English.
Exam registration requirements



All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
The course can be selected for external assessment.
Exam period

The exam takes place

May 31, 2018

at the exam venues of the university.

The exact time of the exam will be informed in the Self-Service at KUnet.

For enrolled students more information about examination, rules, exam schedule, venue etc. is available at the intranet for master students (UK) and master students (DK).



The written reexam takes place

August 23, 2018

If only a few students have registered for the written reexam, the reexam might change to oral including the date, time and place, which will be informed in KUNet or by the Examination Office.


For enrolled students more information about reexamination, rules, re-exam schedule,venue etc. is available at the intranet for master students (UK) and master students (DK)

Criteria for exam assesment

Students are assessed on the extent to which they master the learning outcome for the course.

To receive the top grade, the student must with no or only a few minor weaknesses be able to demonstrate an excellent performance displaying a high level of command of all aspects of the relevant material and can make use of the knowledge, skills and competencies listed in the learning outcomes.

  • Category
  • Hours
  • Lectures
  • 42
  • Preparation
  • 161
  • Exam
  • 3
  • Total
  • 206