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BMAN 70141 Derivative Securities |
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Aims |
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This course introduces students to important financial derivatives, such as forwards, futures, plain-vanilla and more exotic options. It equips students with essential techniques useful for valuing financial deriva- tives and hedging financial risk. The course emphasizes the general principles central to derivatives val- uation, including no-arbitrage arguments and risk-neutral valuation methods, together with their implica- tions for the pricing of financial derivatives. It also discusses some more advantage topics, such as valuing derivatives using Monte-Carlo simulations and finite difference methods, using alternatives to the Black- Scholes model, such as the constant elasticity of variance (CEV) model, the mixed jump-diffusion model, and stochastic volatility models, or calculating a financing institution’s value at risk (VaR). All topics are introduced from an intuitive – and not a mathematically rigorous – perspective. |
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Learning Outcomes |
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On completion of this unit successful students will • Be familiar with the most common derivative contracts traded in financial markets and OTC; • Have some broad knowledge about how derivative contracts have developed over time, are quoted in the financial press, are traded in financial markets, etc.; • Be able to understand, from an intuitive perspective, how derivative securities are valued, using replication approaches, risk-neutral valuation approaches, Monte Carlo valuation or numerical methods (such as the finite-difference or the Longstaff-Schwartz least squares methods); • Be able to understand how derivative securities can be used in financial markets to either in- crease (speculate) or decrease risk (hedging); • Be able to solve standard exercises involving the calculation of derivative values/prices or the optimal number of derivative contracts used for hedging purposes; • Be able to use Monte-Carlo simulations, the implicit and explicit finite difference method, and the Longstaff-Schwartz approach to value more complicated (exotic) derivatives; • Be able to use the simulation or the model-building approach to calculate value-at-risk; • Be able to exercise a capacity for independent and self-managed learning; |
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Methods of feedback to students |
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I provide written and verbal, formative and summative, feedback on the group coursework. One revision session gives students formative feedback on how to improve their examination performance. If students attend that, they enhance their ability to achieve the learning outcomes and perform well on the course. |
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Methods of feedback from students |
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University course evaluation questionnaires. Feedback from appointed student representative(s). |
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Employability |
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The skills developed during the course allow students to work in the investment and asset management industry, either in the role of developing financial instruments or of implementing risk management of these instruments. The course also teaches important skills for students interesting in working in the non-financial sector, for example, as financial officer or controller. The most important of these skills is the hedging of corporate exposures through either direct or indirect hedging techniques. |
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Social Responsibility |
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The course flags up the various dangerous sides of derivatives instruments (as, e.g., the unlimited losses that they can generate), motivating students to think carefully about when and how to use such instruments. As the course is, however, a quantitative course introducing students to the mathematical tools necessary to use and value derivatives, it cannot dwell deeply into the socially undesirable aspects of derivatives. A separate less mathematical course would be needed to that end. |
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Assessment
Group project (25%)
The group project will be handed to you during the course. Each group consists of about five students, with group composition determined by you. If you are unable to find a group, I will of course help you to do so. The data necessary to work on the group project are available from the Blackboard site. In the group project, students are asked to use multiple-step binomial trees, Monte-Carlo simulations, and the finite difference method to value complicated (exotic) derivatives. This will be fun!
The submission deadline is usually Wednesday of “teaching week 13.” In this academic year, that Wednesday would be 18 December 2024. But the date is generally only confirmed by assessments at the start of the academic year, so it is currently preliminary. The project report has to be submitted in soft-copy (no hard-copy). The soft-copy has to be submitted via the course’s Blackboard site. Feedback on the assignment will be given to students until at latest mid-January 2025 (again TBC).
1 ½ hour examination (75%)
There will bean online exam with type-in-a-number, MCQ, and open-ended questions. The exam will take place late in January 2025. The exact exam date is generally released by the university after read- ing week, so in early December. More information to follow.
Overview of sessions
Week 1 (26 September 2024). Introduction to the Course/Forward Contracts
1. Course aim, structure, assessment, etc.
2. Forwards: Definition, payoffs, and market microstructure
3. Forwards: Determination of arbitrage-free forward price
Reading: Chapters 1-2, 5 (the chapter numbers are from the ninth edition of Hull)
Week 2 (3 October 2024). Forwards and Futures
1. Forwards: The forward price is not the forward’s value: Valuation
2. Futures: Definition and comparison with forwards
3. Hedging with futures under basis risk
Reading: Chapters 2, 3, and 5
Week 3 (10 October 2024). Options (Basics/Binomial Tree Valuation)
1. Options: Definition, payoffs/profits, terminology, market microstructure
2. Bounding the value of options: How and why should we be interested?
3. Option valuation using the binomial tree approach
Reading: Chapter 10-11, 13
Week 4 (17 October 2024). Options (Black-Scholes Valuation)
1. What is a stochastic process? Which ones are popular?
2. Deriving the famous Black-Scholes partial differential equation (pde)
3. The Black and Scholes (1973) formula: a. A sketch of the derivation;
b. Using the Black and Scholes (1973) model;
Reading: Chapter 14-15, 17
Week 5 (24 October 2024). The Greeks and Volatility Smiles
1. Setting the stage: A simple example
2. The Greeks: What are they and why are they useful?
3. Delta and Gamma hedging of a portfolio’s value: Examples
4. What is implied volatility: Definition, approximation, put and call parity
5. What does implied volatility imply about the Black-Scholes model?
Reading: Chapter 19-20
Reading Week (28 October - 3 November 2024)
Week 7 (7 November 2024). Basic Numerical Procedures
1. Introduction to Monte-Carlo simulation techniques
2. The explicit and implicit finite difference method
3. Discussion of the coursework assignment (CWA)
Reading: Chapters 21
Week 8 (14 November 2024).Exotic Options
1. Definition and valuation of various exotic options
2. Examples: gaps, choosers, compounds, barriers, binaries, etc.
Reading: Chapter 26
Week 9 (21 November 2024) More on Models and Numerical Methods.
1. More advanced models: CEV, mixed jump-diffusion, and stochastic volatility
2. More advanced binomial tree valuation approaches
3. Longstaff-Schwartz least-squares approach
Reading: Chapter 27
Week 10 (28 November 2024) Value-at-Risk
1. Value-at-Risk: Definition, why important?
2. Simulation-based approach to calculate the VaR
3. Model-Building approach to calculate the VaR
4. Comparison of approaches
Reading: 22
Week 11 (5 December 2024) Revision/Preparation for Exam Paper
1. Revision of course material;
2. A look at a possible exam paper;
Reading: NONE