# GRA 6535 Derivatives

## GRA 6535 Derivatives

This course provides 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 more fancy hedging, exotic derivatives, real options, executive 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 no-arbitrage bounds for derivatives prices
- the binomial option pricing model
- the Black-Scholes model
- delta hedging of options
- hedging options with the Greeks
- extensions of plain vanilla options
- option valuation with stochastic volatility
- empirical performance of option pricing models
- valuation of executive options
- valuation real options
- credit risk valuation using option pricing

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

- identify and arbitrage away violations of model-free no-arbitrage bounds
- identify and arbitrage away violations of option pricing models
- solve the binomial and the Black-Scholes models to value options
- code up option pricing models including models with stochastic volatility and other deviations from Black-Scholes

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

1. Introduction

- Options markets

2. Pricing

- Binomial Trees
- Wiener Processes, Itos Lemma, Black-Scholes-Merton and beyond
- The Greeks

3. Numerical Methods and Applications

- Empirical Performance of Option Pricing Models
- Numerical Techniques
- Exotic Options, Volatility Smiles, Risk Management
- Real Options and Credit Risk

Please note that while attendance is not compulsory in all courses, it is the student’s own responsibility to obtain any information provided in class that is not included on the course homepage/It's learning or text book.

This is a course with continuous assessment (several exam components) and one final exam code. Each exam component is graded by using points on a scale from 0-100. The components will be weighted together according to the information in the course description in order to calculate the final letter grade for the examination code (course). Students who fail to participate in one/some/all exam elements will get a lower grade or may fail the course. You will find detailed information about the point system and the cut off points with reference to the letter grades when the course start.

At resit, all exam components must, as a main rule, be retaken during next scheduled course.

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 spesific prerequisites and will assume that students have followed normal study progression. For double degree and exchange students, please note that equivalent courses are accepted.

Assessments |
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Exam category: Activity Form of assessment: Class participation Weight: 20 Grouping: Individual Exam code: GRA65353 Grading scale: Point scale leading to ECTS letter grade Resit: All components must, as a main rule, be retaken during next scheduled course |

Exam category: Submission Form of assessment: Written submission Weight: 20 Grouping: Group (2 - 3) Duration: 48 Hour(s) Comment: Take-home examination Exam code: GRA65353 Grading scale: Point scale leading to ECTS letter grade Resit: All components must, as a main rule, be retaken during next scheduled course |

Exam category: Submission Form of assessment: Written submission Invigilation Weight: 60 Grouping: Individual Support materials: - BI-approved exam calculator
- Simple calculator
- Bilingual dictionary
Duration: 3 Hour(s) Comment: Written examination with supervision Exam code: GRA65353 Grading scale: Point scale leading to ECTS letter grade Resit: All components must, as a main rule, be retaken during 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.