ECO423 Principles of Derivatives Pricing and Risk Management
The emphasis of the course is on understanding general principles that can be applied to price simple as well as complex derivatives. We use the economic principles and tools to derive closed form formulas, such as the Black-Scholes-Merton model. Because prices of most derivatives cannot be expressed in closed form an important focus of the course is the use of Monte Carlo simulation techniques to estimate derivative prices numerically. 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 principles for pricing derivative assets are based on basic insights that are crucial 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 the binomial model
- Modeling asset prices in continuous time as diffusions
- The Black Scholes model I: the traditional approach (PDEs)
- The Black Scholes model II: the "modern" approach (risk-adjusted probabilities)
- Modeling commodities spot and futures prices
- Fixed income securities
- Real options
- Simulations methods (discretization schemes, Monte Carlo)
- Aspects of financial risk management (Greeks, Value at Risk 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 and 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
- 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
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 (differentiation, and basic integration) and probability theory (expectations, variance, the normal distribution) (as covered in MET1 and MET2). While students need not have recent experience in the use of these concepts, they are expected to master them after they are briefly refreshed in the course.
Requirements for course approval
Students must do four spreadsheet-based simulation projects. One of these projects (announced in the course) must be handed in, and be of passable quality.
Four-hour written school exam. The exam will be given in English and must be answered in English.
Grading scale A - F.
Reference textbook: John Hull, Options, Futures, and Other Derivatives, Prentice Hall (latest edition)
Notes and articles.
- ECTS Credits
- Teaching language
Spring. Offered spring 2019.
Associate Professor Jørgen Haug, Department of Finance, NHH.