ECO423 Advanced Derivatives
Spring 2024

Topics
In the course we develop 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 is the use of Monte Carlo simulation 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 master tools that are important for determining appropriate financial risk management strategies.
Topics:
 Repetition of key insights from the binomial model
 A general model of asset prices: continuoustime diffusions
 Pricing via the replicating portfolio argument
 Pricing directly via riskadjusted 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

Learning outcome
After successful completion of the course the student can:
Knowledge
 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 riskadjusted probabilities
 appreciate strengths and weaknesses of popular risk measures, like "the Greeks", Value at Risk and Expected Shortfall
Skills
 formulate, interpret, and work with continuoustime models (diffusions)
 analyse and solve realistic/complex valuation problems
 critically evaluate and implement financial risk management methods
 implement pricing and risk management tools in R or Excel
General competence
 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

Teaching
Regular lectures, student case presentations

Recommended prerequisites
The course does not assume or require prior programming skills, but does illustrate key ideas via programming examples in R. Prior knowledge of R, or basic programming skills in some other language, are thus helpful but not required.

Required prerequisites
Students are expected to have a basic knowledge of key valuation concepts, like present value, the CAPM, and securities 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.

Compulsory Activity
Students must complete several group projects, and submit corresponding self assessment reports. Students are free to use either Excel or R to complete the projects.

Assessment
Four hours individual home exam. The exam must be answered in English.

Grading Scale
AF.

Computer tools
The use of R is encouraged, but not required. Some key methods are illustrated through programming examples in R.

Literature
Reference textbook: John Hull, Options, Futures, and Other Derivatives, Prentice Hall (latest edition)
Notes and articles.
Overview
 ECTS Credits
 7.5
 Teaching language
 English
 Semester

Spring. Offered spring 2024.
Course responsible
Associate Professor Jørgen Haug, Department of Finance, NHH.