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Introduction to financial modeling

Autumn 2012

General Information

This course gives an introduction to mathematical finance, with an emphasis on modeling.

Contents

  • Introduction to financial markets, basics of equities, commodities, foreign-exchanges, forward and futures.
  • Options, payoff diagram, put-call parity, trading strategies with options.
  • Poisson process and Brownian motion, introduction to stochastic differential equations, Ito calculus, Wiener, Orstein -Uhlenbeck, Langevin equation, introduction to martingales, examples of common models used in finance, risk neutral pricing, Fynman-Kac formula.
  • Black-Scholes model and the Greek letters.
  • Volatility problem, implied volatility, smile dynamics, leverage effect, heteroskedasticity, introduction to Garch and stochastic volatility models.
  • Inference problems.
  • System identification in finance, parametric, semi/non parametric, maximum likelihood, EM.
  • Some advanced topics and course summary.

    • Organization and Examination

    This course gives 9 hp.  The proposed course consists of lectures and related computer exercises. There is no written exam for the course and instead the students are supposed to submit their solutions to the exercises in the form of reports.

    Lectures

    The standard two hour lectures. The lectures will be given in Algoritmen (B - Building, between entrance 27 and 29, corridor A).

    Computer Exercises

    The course is going to include extensive computer exercises.

    Project (optional)

    One can receive an additional 3 hp  by carrying out a project, which can take place after the course is finished. More information will be given during the course.

     

    Course Literature

    The main books to be used during the course are, 
    [1] John C. Hull,  Options, Futures and other derivatives.

    [2] T. C.  Gard, Introduction to Stochastic Differential Equations.

    Additional references : 

    [3] Davis M.H.A., Linear Estimation and Stochastic Control.

    [4] Bernt Øksendal, Stochastic Differential Equations: An Introduction with Applications.

    [5] Paul Wilmott, Paul Wilmott Introduces Quantitative Finance.

    [6] Thomas Björk, Arbitrage Theory in Continuous Time.

     

     

    Prerequisites

    Basic knowledge in linear algebra and  probability theory. For the computer exercises, a fair skill in coding (e.g., MATLAB) is assumed.

    Related Courses

    System identification, Sensor fusion. Machine learning

    Contact Persons

    Dr. Jesica Escobar, tel 013 - 284027, email: escobar_at_isy.liu.se

    Dr.  Saikat Saha, tel 013 - 284027, email: saha_at_isy.liu.se.

     

     

     


    Page responsible: Escobar J. and Saha S.
    Last updated: 2012-12-07