Derivatives and Risk Management

Study Board of Market and Management Anthropology, Economics, Mathematics-Economics, Environmental and Resource Management

Teaching language: English
EKA: B560008112, B560008102
Censorship: Second examiner: None
Grading: Pass/Fail, 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Master

Course ID: B560008101
ECTS value: 10

Date of Approval: 12-03-2024


Duration: 1 semester

Course ID

B560008101

Course Title

Derivatives and Risk Management

Teaching language

English

ECTS value

10

Responsible study board

Study Board of Market and Management Anthropology, Economics, Mathematics-Economics, Environmental and Resource Management

Date of Approval

12-03-2024

Course Responsible

Name Email Department
Charlotte Sun Clausen-Jørgensen chcla@sam.sdu.dk Finance (FIN)

Offered in

Odense

Level

Master

Offered in

Autumn

Duration

1 semester

Recommended prerequisites

This course requires that the student has prior knowledge of financial markets, financial instruments, and derivatives. The student must be able to compute the present value of a certain stream of cash flows (e.g. from a bond) using the term structure of zero-coupon bond yields. For uncertain cash flow streams one should be able to use risk neutral valuation to compute their values in a binomial model. Understanding how various derivatives (e.g. forwards, futures, swaps, and options) work is also a prerequisite, e.g. one must be able to draw a payoff diagram for an option and explain how it works. These are all competences acquired in the course "Finansiering, investing og virksomhedsstrategi" (course no. 9161001) which is based on the textbook:
  • David Hillier, Mark Grinblatt and Sheridan Titman: Financial Markets and Corporate Strategy, European Edition, Irwin/McGraw-Hill, latest edition.

Furthermore, the student should have an elementary background in mathematics and probability theory. In particular one should be able to compute expectations, variances, and covariances of random variables whether their distribution is discrete (e.g. binomial) or continuous (e.g. normal). One also need to know elementary rules of differentiation and integration, e.g. the chain rule for differentiation of composite functions. Finally, it is highly recommended that the student is familiar with vector and matrix notation and know how to solve a system of linear equations. These are all competences acquired in the courses "Matematik" (course no. 9105701) and "Statistik" (course no. 9116001) which are based on the textbooks:
  • Knut Sydsaeter and Peter Hammond, Essential Mathematics for Economic Analysis, Pearson Education, latest edition.
  • Malcow-Møller, N. og Allan Würtz "Indblik i Statistik", latest edition.

Aim and purpose

The course gives students a thorough understanding of derivatives, their applications, and selected models for the pricing and risk management of derivatives. For the pricing of stock options, the Black-Scholes-Merton model and some alternatives are presented. Thus, students must become familiar with stochastic calculus. An overview of fixed income securities is given. Various popular models for the pricing of bonds and derivatives on bonds and interest rates are discussed. An introduction to numerical techniques frequently applied in derivatives pricing problems is also given.

Content

  • Forwards and futures
  • Stock options: general properties and specific models (the binomial model, the Black-Scholes-Merton model and alternative models)
  • Hedging and risk management with options
  • Risk-neutral pricing and absence of arbitrage
  • Bonds, yield curves, and interest rate derivatives
  • Models of the term structure of interest rates
  • Interest rate risk management
  • Numerical methods: trees, finite differences, Monte Carlo simulation
  • Stochastic (Itô) calculus 

Description of outcome - Knowledge

Demonstrate knowledge about the course’s focus areas enabling the student to

  • Describe and compare the payoffs and practical applications of forwards and futures.
  • Explain how forward prices and futures prices can be computed,
  • Describe the payoffs and practical applications of European and American call and put options on stocks.
  • Describe when early exercise of American options can be optimal.
  • Explain how stock prices are modelled in the binomial and Black-Scholes-Merton models.
  • Explain how replicating portfolios and option prices can be computed in the binomial and Black-Scholes-Merton models.
  • Criticise and reflect over the crucial assumptions in the binomial and Black-Scholes-Merton models
  • Describe implied volatility smiles and provide potential explanations of such smiles.
  • Describe alternative models for stock option pricing and compare them to the Black-Scholes-Merton model.
  • Describe the so-called Greek letters in relation to option pricing and explain how delta, theta, and gamma are related
  • Explain the concept of arbitrage and why the absence of arbitrage implies that a derivative asset can be priced by computing a conditional expectation of the properly discounted payoff under a risk-adjusted probability measure or, in some cases, by solving a specific partial differential equation.
  • Explain basic bond market terminology
  • Describe the payoffs, practical applications, and general pricing results of interest rate forwards and futures, Eurodollar-futures, bond options, caps, floors, collars, swaps, and swaptions
  • Explain and criticize selected continuous-time models of the term structure of interest rates
  • Explain how interest rate risk can be measured and managed using popular continuous-time models of the term structure of interest rates.
  • Explain how selected numerical methods (binomial/trinomial trees, finite difference solutions of partial differential equations, Monte Carlo simulation) can be applied to the pricing of derivatives in selected models and reflect over the applicability of the different methods.  

Description of outcome - Skills

Demonstrate skills, such that the student is able to:
  • Derive forward and futures prices, and identify when and how the price of a futures contract differs from the price of an otherwise identical forward contract
  • Derive the put-call parity
  • Apply the binomial and Black-Scholes-Merton models for stock option pricing.
  • Derive pricing formulas and replicating portfolios in the binomial and Black-Scholes-Merton model.
  • Derive the fundamental partial differential equation and solve it in the Black-Scholes-Merton model and in similar frameworks.
  • Compute implied volatility smiles
  • Apply alternative models for stock option pricing and compare them to the Black-Scholes-Merton model.
  • Apply the Greek letters to hedging and risk management.
  • Compute, and relate bond prices, bond yields, and the term structure of interest rates.
  • Extract yield curves from bond prices
  • Derive general pricing results of interest rate forwards and futures, Eurodollar-futures, bond options, caps, floors, collars, swaps, and swaptions, and derive relations between these derivative securities.
  • Derive the fundamental partial differential equation and pricing formulas for selected interest rate derivatives within selected continuous-time models of the term structure of interest rates.
  • Compare selected continuous-time models of the term structure of interest rates.
  • Compute dynamic interest rate risk measures and apply them to interest rate risk management.
  • Compare dynamic interest rate risk measures to the classical Macaulay and Fisher-Weil risk measures.
  • Implement selected numerical methods (binomial/trinomial trees, finite difference solutions of partial differential equations, Monte Carlo simulation) and apply them to the pricing of derivatives in selected models.
  • Apply Itô calculus. 

Description of outcome - Competences

Demonstrate competences, such that the student is able to:
  • Identify theoretical or practical applications on which the knowledge and skills obtained above can be applied independently.
  • Apply the knowledge and skills obtained above in an interdisciplinary application (e.g., within asset pricing, corporate finance, econometrics, or accounting).
  • Use the above knowledge and skills to participate in team work so that the student obtains competences in collaboration and communication. 
  • Explain the relevant theory and perform analysis in relation to the content of the course. 
  • Explain assumptions and derivations used in the student’s analysis, e.g., elaborate on methods, models, calculations, formulas, etc. 

Literature

Examples:

  • Chapters from Hull, J.C.: "Options, Futures, and Other Derivatives", Prentice Hall, newest edition, or similar material.
  • Chapters from Munk, C.: "Fixed Income Modelling", Oxford University Press, newest edition.
  • Articles and lecture notes. 

Teaching Method

The course will be a mix of class room lectures (where some lectures can be online), and exercises.

Workload

Scheduled classes:
4 hours of lectures (2x2) weekly for 11.5 non-consecutive weeks.
The lecturing period can be extended due to intervening project or assignment work.
2 hours of exercises for 13 weeks. 

Workload:
The students' workload is expected to be distributed as follows: 
  • Lectures - 46 hours 
  • Preparation, lectures - 92 hours
  • Class exercises - 26 hours
  • Preparation, exercises - 52 hours
  • Assignments - 49 hours
  • Examination - 5 hours

Total 270 hours.

This corresponds to an average weekly workload of 13 hours during the semester, including the exam.

Examination regulations

Exam

Name

Exam

Timing

Portfolio assignments (part 1)

Exam: During the semester
Reexam: February


Written exam (part 2)

Exam: January
Reexam: February

Tests

Portfolio assignments (part 1)

Name

Portfolio assignments (part 1)

Form of examination

Portfolio

Censorship

Second examiner: None

Grading

Pass/Fail

Identification

Student Identification Card - Date of birth

Language

English

Duration

During the semester

Length

No limitations.

Examination aids

All exam aids allowed.

Assignment handover

The assignment is handed over in Digital Exam or Itslearning.

Assignment handin

Electronic hand-in via Digital Exam or Itslearning.

ECTS value

1

Additional information

Part 1 consists of three written assignments that are handed out during the semester.

Part 1 is passed on the basis of an overall assessment of an acceptable level, approximately equivalent to 50%. It is a necessary, but not sufficient, condition for passing that each written assignment has at least 25% correct answers.

The assignments are solved in groups of 3 students. The lecturer can dispense from this and can also allocate students.

The examination and assessment can be carried out by one or more of the lectures involved in the course.

Re-examination

Form of examination

Oral examination

Identification

Student Identification Card - Date of birth

Duration

20 minutes.

Examination aids

All examination aids allowed. 

Additional information

Individual oral examination (20 minutes without preparation) based on the assignments in the ordinary exam for part 1, but it can also include questions in other topics within the syllabus.

The reexam will be conducted with an internal second examiner. 
The examination and assessment can be carried out by one or more of the lectures involved in the course.

The examination tests the students' achievement on all specified targets.

EKA

B560008112

Written exam (part 2)

Name

Written exam (part 2)

Form of examination

Written examination on premises

Censorship

Second examiner: None

Grading

7-point grading scale

Identification

Student Identification Card - Exam number

Language

English

Duration

5 hours

Length

No limitations

Examination aids

All exam aids allowed. However, it is not allowed to communicate with anybody. 

Assignment handover

The assignment is handed over in Digital Exam.

Assignment handin

Electronic hand-in via Digital Exam.

ECTS value

9

Additional information

Exam form for international exchange students: 10-hours take-home assignment.
Date for submission will appear from the examination plan.

The examination tests the students' achievement on all specified targets. 

The examination and assessment can be carried out by one or more of the lectures involved in the course.

Re-examination

Form of examination

Oral examination with preparation

Identification

Student Identification Card - Date of birth

Preparation

20 minutes.

Duration

20 minutes.

Examination aids

All exam aids are allowed at the preperation. 

Assignment handover

In the examination room. 

Additional information

The examination is based on a randomly drawn topic, but can also include questions in other topics from the syllabus.

The reexam will be conducted with an internal second examiner. 
The examination and assessment can be carried out by one or more of the lectures involved in the course.

The examination tests the students' achievement on targets by random check.

EKA

B560008102

Transitional rules

Used examination attempts in the former identical course will be transferred.

Courses that are identical with former courses that are passed according to applied rules cannot be retaken.

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