Stochastic Calculus and Finance

  • Typ: Vorlesung
  • Lehrstuhl: Statistik, Ökonometrie und Mathematische Finanzwirtschaft
  • Semester: WS 2012/2013
  • Ort:

    Geb. 20.13, 006 (V)
    Geb. 20.13, 006 (Ü)

  • Zeit:

    Freitag, 09:45 – 11:15 (V)
    Freitag, 11:30 – 13:00 (Ü)

  • Beginn: 19.10.2012
  • Dozent:


  • SWS: 4
  • LVNr.: 2521331
  • Prüfung: Mündlich, nach Vereinbarung
  • Hinweis:

    To be held in English

    The course will provide rigorous yet focused training in stochastic calculus and mathematical finance. Topics to be covered:
    1. Stochastic Calculus: Stochastic Processes, Brownian Motion and Martingales, Stopping Times, Local martingales, Doob-Meyer Decomposition, Quadratic Variation, Stochastic Integration, Ito Formula, Girsanov Theorem, Jump-diffusion Processes, Stable and tempered stable processes. Levy processes.
    2. Mathematical Finance: Pricing Models, The Black-Scholes Model, State prices and Equivalent Martingale Measure, Complete Markets and Redundant Security Prices, Arbitrage Pricing with Dividends, Term-Structure Models (One Factor Models, Cox-Ingersoll-Ross Model, Affine Models), Term-Structure Derivatives and Hedging, Mortgage-Backed Securities, Derivative Assets (Forward Prices, Future Contracts, American Options, Look-back Options), Option pricing with tempered stable and  Levy-Processes and volatility clustering,  Optimal Portfolio and Consumption  Choice (Stochastic Control and Merton continuous time optimization  problem), Equilibrium models, Consumption-Based CAPM, Numerical Methods.

    1. Dynamic Asset Pricing Theory, Third Edition by Darrell Duffie, Princeton University Press, 1996
    2. Stochastic Calculus for Finance II: Continuous-Time Models by Steven E. Shreve, Springer, 2003
    3. An Introduction to Stochastic Integration (Probability and its Applications) by Kai L. Chung , Ruth J. Williams, Birkhäuser,
    4. Methods of Mathematical Finance by Ioannis Karatzas, Steven E. Shreve, Springer, 1998
    5. Kim Y.S. ,Rachev S.T. ,Bianchi M-L, Fabozzi F.  Financial market models with Levy processes and time-varying volatility, Journal of Banking and Finance, 32/7, 1363-1378,  2008.