Advanced Derivatives

ECO423 Advanced Derivatives

Autumn 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.


    • Repetition of key insights from the binomial model
    • A general model of asset prices: continuous-time diffusions
    • Pricing via the replicating portfolio argument
    • 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

  • Learning outcome

    After successful completion of the course the student can:


    • 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 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


  • 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.


ECTS Credits
Teaching language

Spring. Offered spring 2024.

Course responsible

Associate Professor Jørgen Haug, Department of Finance, NHH.