GRA 6535 Derivatives

GRA 6535 Derivatives

Course code: 
GRA 6535
Course coordinator: 
Tong Zhang
Course name in Norwegian: 
Product category: 
MSc in Finance
2023 Autumn
Active status: 
Level of study: 
Teaching language: 
Course type: 
One semester

This course provides a thorough understanding of the workings and pricing of derivative securities.

We cover model-free no-arbitrage bounds for derivatives prices, the binomial model and its continuous time limit, the mathematics of continuous time, the Black-Scholes model and its derivation, adjusting the Black-Scholes and binomial models to price futures and currency options, delta hedging and other hedging techniques, exotic derivatives, real options, credit risk, etc. A significant part of the course focuses on the numerical valuation of options.

Learning outcomes - Knowledge

By the end of the course the students are expected to know:

  • model-free, binomial, and Black-Scholes pricing of options
  • hedging of options
Learning outcomes - Skills

By the end of the course the students are expected to be able to:

  • value standard and exotic options using formulas or simple trees
  • code up option pricing models as trees or use Monte Carlo
General Competence

The students by the end of the course are expected to be able to understand the workings and limitations of option pricing theory.

Course content

1. Introduction

  • Options markets
  • Model-free no-arbitrage bounds
  • Trading strategies with options

2. Pricing

  • Binomial trees
  • Wiener processes, Ito's lemma, Black-Scholes-Merton and beyond
  • The Greeks

3. Numerical Methods and Applications

  • Empirical performance of option pricing models, volatility smiles
  • Numerical techniques, exotic options
  • Real options, credit Risk
  • International derivatives markets
Teaching and learning activities

Mostly lectures with theory, examples, in-class discussion, and exercises.

Software tools
Additional information

This course has mandatory coursework requirements: Two assignments. The coursework requirements must be approved to be able to sit for the exam.

The exam for this course has been changed starting academic year 2023/2024. The course now has one ordinary exam (in addition to mandatory coursework requirements). It is not possible to retake the old version of the exam. 

It is the student’s own responsibility to obtain any information provided in class.

Honour Code
Academic honesty and trust are important to all of us as individuals, and represent values that are encouraged and promoted by the honour code system. This is a most significant university tradition. Students are responsible for familiarizing themselves with the ideals of the honour code system, to which the faculty are also deeply committed. Any violation of the honour code will be dealt with in accordance with BI’s procedures for cheating. These issues are a serious matter to everyone associated with the programs at BI and are at the heart of the honour code and academic integrity. If you have any questions about your responsibilities under the honour code, please ask.


All courses in the Masters programme will assume that students have fulfilled the admission requirements for the programme. In addition, courses in second, third and/or fourth semester can have specific prerequisites and will assume that students have followed normal study progression. For double degree and exchange students, please note that equivalent courses are accepted.


Deviations in teaching and exams may occur if external conditions or unforeseen events call for this.

Required prerequisite knowledge

College-level calculus (limit, differentiation, integration, Taylor expansion, etc), probability theory (cdf and pdf, common distributions, expectation, variance, etc), and basic knowledge in R or similar programming languages, such as python and matlab (matrix indexation, basic operations, loop, if, plot, etc).

Mandatory courseworkCourseworks givenCourseworks requiredComment coursework
Mandatory22Two assignments. Both assignments must be approved to be eligible for the final exam.
Mandatory coursework:
Mandatory coursework:Mandatory
Courseworks given:2
Courseworks required:2
Comment coursework:Two assignments. Both assignments must be approved to be eligible for the final exam.
Exam categoryWeightInvigilationDurationSupport materialsGroupingComment exam
Exam category:
Form of assessment:
Written submission
Exam code:
GRA 65353
Grading scale:
Grading rules:
Internal examiner
Examination when next scheduled course
100Yes2 Hour(s)
  • Bilingual dictionary
Individual Written examination under supervision
Exam category:Submission
Form of assessment:Written submission
Grouping (size):Individual
Support materials:
  • Bilingual dictionary
Duration:2 Hour(s)
Comment:Written examination under supervision
Exam code:GRA 65353
Grading scale:ECTS
Resit:Examination when next scheduled course
Type of Assessment: 
Ordinary examination
Total weight: 
Sum workload: 

A course of 1 ECTS credit corresponds to a workload of 26-30 hours. Therefore a course of 6 ECTS credits corresponds to a workload of at least 160 hours.