5497 Continuous Time Finance
em.o.Univ.Prof. Dr. Josef Zechner, Prof. Dr. Tomas Björk
Contact details
Weekly hours
Language of instruction
02/01/19 to 02/28/19
Registration via LPIS
Notes to the course
Day Date Time Room
Monday 05/06/19 10:00 AM - 03:00 PM D4.4.008
Tuesday 05/07/19 10:00 AM - 03:00 PM D4.4.008
Wednesday 05/08/19 10:00 AM - 03:00 PM D4.4.213
Thursday 05/09/19 10:00 AM - 03:00 PM D4.4.008
Monday 05/13/19 10:00 AM - 03:00 PM D4.4.008
Tuesday 05/14/19 10:00 AM - 03:00 PM D4.4.008
Wednesday 05/15/19 10:00 AM - 03:00 PM D4.4.213

1. Extensions of the Black-Scholes model: Dividends, currency derivatives.

2. Incomplete markets: Pricing in a factor model, the market price of risk.

3. The martingale approach to arbitrage pricing. Martingale measures. The first and second fundamental theorems.

4. Interest rate theory: Short rate models, affine term structures, inversion of the yield curve, forward rate models, the HJM approach.

5. Change of numeraire: The normalized economy, pricing in a new numeraire, forward measures, the general option pricing formula, forward and futures contracts.

6. LIBOR and swaption market models.


Slides II

Lecture notes


Learning outcomes
The objective of the course is to present the fundamentals of arbitrage theory for pricing contingent claims in continuous time.
Teaching/learning method(s)
Whiteboard, open discussions, presentations by students. Lecture notes are available.
Grades are based on the (quality of) solution of exercises, presentations, and a final written test.
Prerequisites for participation and waiting lists

More precisely the students are assumed to have basic knowledge of the following mathematical areas:

• Measure and integration theory, including the Radon Nikodym theorem

• Stochastic differential equations

• The Kolmogorov backward equation

• The Feynman-Kac representation Theorem• The Ito formula

• The Girsanov Theorem

• The stochastic integral representation Theorem for Wiener martingalesThe students are also assumed to be familiar with elementary theory for arbitrage free pricing and hedging of European derivatives within the Black-Scholes model.

1 Author: Tomas Björk:
Title: "Arbitrage Theory in Continuous Time",

Publisher: Oxford University Press
Edition: 2nd ed.
Year: 2004
Availability of lecturer(s)
Office hours by appointment email
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Last edited: 2019-02-18