Principles of Derivatives Pricing and Risk Management

ECO423 Principles of Derivatives Pricing and Risk Management

Autumn 2018

Spring 2019
  • Topics

    The course introduces students to advanced techniques for pricing derivative securities, using tools from continuous-time finance. The emphasis is on understanding unifying principles that can be applied to determine the price of simple as well as complex derivative securities. The associated techniques are the basic tools necessary to derive closed form formulas, such as the Black-Scholes-Merton model. Because prices of most contracts cannot be expressed in closed form a second focus of the course is the use of simulation techniques to implement the valuation principles. The obvious application of the techniques is to price financial contracts, like futures, options, swaps, etc. The same techniques can also be applied to estimate the present value of real assets essential in firms' investment decisions. The principles are then referred to as "real options theory", which is an important applied topic in the course. The principles for pricing derivative securities are based on basic insights that are crucial in risk management. By mastering techniques for pricing the securities, the students will thus also get access to tools necessary for determining useful 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
    • Real options
    • Simulations methods (discretization schemes, Monte Carlo)
    • Aspects of financial risk management (Greeks, Value at Risk etc)

  • Learning outcome

    After taking the course students should be able to estimate the value of complex financial contracts. They should moreover be able to identify real projects that can be analyzed using the toolbox acquired during the course. Finally, students should be able to critically evaluate and implement financial risk management techniques. They should in particular:

    • Understand the economic intuition behind option pricing; the roles of no arbitrage and replicating portfolios
    • Be able to set up and work with continuous-time models of asset prices (diffusions)
    • Be able to derive fundamental partial differential equations (PDEs) for derivative securities, and the associated expression for their present value (the Feynman-Kac solution)
    • Understand the economic motivation and intuition behind Equivalent Martingale Measures (EMM), as well as their application to asset pricing
    • Be able to apply PDE and EMM techniques to determine present values of contingent claims by means of simulation techniques
    • Understand the application of simulation techniques in risk management, and the different roles played by physical and risk-adjusted probabilities

  • Teaching

    Regular lectures.

  • Required prerequisites

    Students should already have skills in probability theory similar to that covered in MAT013 or VOA038 to take this course. FIE425 (derivatives and risk management) and ECO421 (asset pricing) offer less technical background for the topics covered in this course.

  • Assessment

    Four hour written school exam. The exam will be given in English and has to be answered in English.

  • Grading Scale

    Grading scale A - F.

  • Computer tools


  • Literature

    Reference textbook: John Hull, Options, Futures, and Other Derivatives, Prentice Hall (latest edition)

    Notes and articles.


ECTS Credits
Teaching language


Course responsible

Jørgen Haug, Department of Finance