ECO423 Advanced Derivatives
The course develops general methods that can be applied to value simple as well as complex derivatives. Because prices of most derivatives cannot be expressed in closed form an important topic in the course is the use of Monte Carlo simulation techniques to numerically estimate prices. While the obvious application of the techniques is to price financial contracts, like futures, options, swaps, etc., the same techniques can be applied to estimate the present value of real assets; an important input in firms' investment decisions. When applied to real assets the principles are referred to as "real options methods", which is an important applied topic in the course. The methods for pricing derivatives rely on insights that are crucial also in risk management. By mastering techniques for pricing derivatives, students will thus also work with tools that are important for determining appropriate financial risk management strategies.
- Repetition of key insights from the binomial model
- A general model of asset prices: continuous-time diffusions
- Pricing via the replicating portfolio argument of Black and Scholes, and Merton
- Pricing directly via risk-adjusted probabilities: Martingale methods
- Simulations methods (discretization schemes, Monte Carlo), in R or Excel
- Modeling commodities spot and futures prices
- Fixed income securities
- Stochastic volatility
- Real options
- Financial risk management and its pitfalls: Greeks, Value at Risk, Expected Shortfall, etc
After successful completion of the course the student will
- understand the key economic principles of option pricing theory: no arbitrage, replicating portfolios, PDEs, equivalent martingale measures
- understand the limits and strengths of traditional present value methods versus option pricing methods
- understand the role of simulation techniques in valuation and risk management, and the different roles played by physical and risk-adjusted probabilities
- appreciate strengths and weaknesses of popular risk measures, like "the Greeks", Value at Risk and Expected Shortfall
- formulate, interpret, and work with continuous-time price models (diffusions)
- analyse and solve complex valuation problems
- critically evaluate and implement financial risk management methods
- implement pricing and risk management tools in R or Excel
- analyse advanced valuation problems in both the real and financial sector
- implement advanced valuation and risk management methods, using appropriate computer tools
- communicate with sophisticated professionals, and function at a high level both as a user and provider of derivatives
It will be possible to follow the course digitally.
The course does not assume or require prior programming skills, but does illustrate some key ideas via programming examples in R. Prior knowledge of R, or basic programming skills in some other language, will be helpful to appreciate the programming illustrations.
Students are expected to have a basic knowledge of key valuation concepts, like present value, the CAPM, and financial assets like bonds, stocks, calls, and puts (for instance at the level of FIE400). Students must have completed a basic course in mathematics, and probability theory or statistics. While students need not have recent experience in the use of concepts from such courses, they are expected to master them after they are briefly refreshed in the course.
Requirements for course approval
Students must do four simulation projects, in either Excel or R. One of these projects (announced in the course) must be handed in, and be of passable quality.
Individual home exam, four hours. The exam must be answered in English.
Grading scale A - F.
The use of R is encouraged, but not required. Some key methods are illustrated through programming examples in R.
Reference textbook: John Hull, Options, Futures, and Other Derivatives, Prentice Hall (latest edition)
Notes and articles.
- ECTS Credits
- Teaching language
Spring. Offered spring 2021.
Associate Professor Jørgen Haug, Department of Finance, NHH.