GRA 6535 Derivatives
GRA 6535 Derivatives
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.
By the end of the course the students are expected to know:
- model-free, binomial, and Black-Scholes pricing of options
- hedging of options
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
The students by the end of the course are expected to be able to understand the workings and limitations of option pricing theory.
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
Mostly lectures with theory, examples, in-class discussion, and exercises.
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. It is not possible to retake the old version of the exam. For questions regarding previous results, please contact InfoHub.
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.
Disclaimer
Deviations in teaching and exams may occur if external conditions or unforeseen events call for this.
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 coursework | Courseworks given | Courseworks required | Comment coursework |
|---|---|---|---|
| Mandatory | 2 | 2 | Two assignments. Both assignments must be approved to be eligible for the final exam. |
| Assessments |
|---|
Exam category: School Exam Form of assessment: Written School Exam - pen and paper Exam/hand-in semester: First Semester Weight: 100 Grouping: Individual Support materials:
Duration: 2 Hour(s) Exam code: GRA 65353 Grading scale: ECTS Resit: Examination when next scheduled course |
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.