Instructors:	Mag. Florian Löcker, em.o.Univ.Prof. Dr. Helmut Strasser
Type:	PI
Weekly hours:	2
Members (max.):	15
Registration period:	04/26/10 to 05/02/10
Note:	Die Lehrveranstaltung wird nur im SS angeboten.

Class objective(s) (learning outcomes)

Continuous time finance is concerned with: Brownian motion, stochastic calculus, risk-neutral pricing, stochastic and partial differential equations, exotic options.

After completing this class the student will have the ability to:

• describe the basic concepts and methods of continuous time finance;
• apply and do computational work with the basic concepts and definitions of continuous time finance.

After completing this class the student will also have the ability to:

• confidently apply ideas of continuous time finance in doing analytical work for financial markets.
• solve applied problems where skills are required from continuous time finance.

Prerequisites according to degree program

• Successful completion of the classes „Mathematics I“ and „Financial Markets and Instruments“.

Teaching and learning method(s)

This class is taught as a lecture accompanied with homework assignments.

The lectures are aimed at providing and explaining the basic concepts and definitions, while the homework assignments (distributed every week) will help students to comprehend the key ideas of the lectures and have to be solved using an interactive wikipedia framework via internet, admitting authorized contributions and discussions. The homework assignments will be based on the week’s lecture and will include relevant mathematical problems that have to be solved. The discussions and homework solutions are at least every week checked by the lecturer.

In case of restricted admission; selection criteria

• Advanced Business Mathematics (class Mathematics I of the QFin program);
• Advanced Business Probability theory (class Probability of the QFin program);
• Basic statistical computing (class Statistics I of the QFin program).

Criteria for successful completion

• written midterm test (weight: 40%)
• written endterm test (weight: 30%)
• homework assignments and group discussions (weight: 30%)

The assessment of the home assignment will be based on the number and the quality of the authorized contributions, both solutions and comments.

Availability of instructor(s) for contact by students

mailto:helmut.strasser@wu.ac.at
mailto:florian.loecker@wu.ac.at

Miscellaneous

Course Reading:

The contents of the course are covered by the following reference:

[S] S.E. Shreve (2004). Stochastic Calculus for Finance II: Continuous-Time Models. Springer Finance. Springer Verlag. ISBN 978-0-387-40101-0

Day	Date	Time	Room
Monday	05/03/10	08:30 AM - 12:00 PM	SR Statistik (2H415)
Thursday	05/06/10	08:30 AM - 12:00 PM	SR Statistik (2H415)
Monday	05/10/10	08:30 AM - 12:00 PM	SR Statistik (2H415)
Monday	05/17/10	08:30 AM - 12:00 PM	SR Statistik (2H415)
Thursday	05/20/10	09:00 AM - 11:00 AM	SR Statistik (2H415)
Thursday	05/27/10	08:30 AM - 12:00 PM	SR Statistik (2H415)
Monday	05/31/10	08:30 AM - 12:00 PM	SR Statistik (2H415)
Monday	06/07/10	08:30 AM - 12:00 PM	SR Statistik (2H415)
Thursday	06/10/10	09:00 AM - 11:00 AM	SR Statistik (2H415)

After attending this session and studying its contents sufficiently students should be able to define the following concepts, to comprehend them and explain their meaning, to state and explain the main ideas concerning the concepts, and to solve problems applying the concepts:

Unit	Contents
1	Unit 1: Brownian Motion Random walk – limit of random walks - Brownian motion – martingale property – quadratic variation – geometric Brownian motion Black Scholes formula - Markov property – first passage times – reflection principle References: S chapter 3
2	Unit 2: Stochastic calculus I Ito integral – Ito formula – Ito processes – evolution of the portfolio value – evolution of the option value - application to Black Scholes model – Greeks – put call parity – stochastic differential equation - Vasicek model – self financing trading References: S chapter 4
3	Unit 3: Stochastic calculus II Multiple Brownian motion – Ito formula for multiple processes – Levy’s characterization – decomposition of correlated Brownian motions – creating correlated Brownian motions – instantaneous correlation - Brownian bridge References: S chapter 4
4	Unit 4: Risk-Neutral Pricing I Girsanov’s theorem – risk neutral measures – state price density - prices under the risk neutral measure – martingale respresentation – hedging with one stock – implying the risk neutral distribution References: S chapter 5
5	Unit 5: Risk-Neutral Pricing II Multivariate Girsanov’s theorem – multidimensional market models – correlation under change of measures – existence of risk neutral measures – uniqueness of risk neutral measures – dividend paying stocks – forwards and futures References: S chapter 5
6	Unit 6: Stochastic differential equations and partial differential equations Stochastic differential equations – solution of linear stochastic differential equations – Hull White model – Cox Ingersoll Ross model – affine models - Feynman Kac formulas – Heston model References: S chapter 6
7	Unit 7: Exotic Options Barrier options – lookback options – asian options – risk neutral pricing via Monte Carlo methods References: S chapter 7