Mathematical Finance: Discrete and Continuous Time Models

Lecturers:	Prof. Dr. Freddy Delbaen Prof. Dr. Thorsten Rheinländer PD Dr. Uwe Schmock Prof. Dr. Philipp J. Schönbucher
Location:	ETHZ, HG D3.2
Time:	Mo. 15.15 - 17.00
First lecture:	October 28, 2002
Language:	English

Contents:

Subjective and synthetic probability measures
Bank account, numéraire
Stock price processes, discounting
Trading strategies, self-financing property
Set of discounted trading gains
Definition of arbitrage
Localization of arbitrage in time
Price functionals
Equivalent martingale measures (with bounded density)
Theorem of Dalang, Morton and Willinger
Minimal and maximal prices of contingent claims
Markovian Models
Existence of martingale measures preserving the Markov property
Call and put options in the binomial model
Passage to to limit in a scaled binomial model
Derivation of the Black-Scholes formula
Call-put parity
Complete markets and uniqueness of the equivalent martingale measure
American options
Forward contracts, hedge
Futures and their relation to forwards
Distribution of certain hitting times of Brownian motion with drift
Black-Scholes option-pricing theory
European and American options

Grades: The grades for participants of the MAS Finance program will be based on a written examination. The examination is scheduled for Thursday, March 27, 2003, from 10-12 in lecture theatre HG G5, ETH main building. The examination is closed books, no notes, no pocket calculator, no mobile phone, only white paper and a ball pen.

Literature:

David Williams: Probability with Martingales, Cambridge University Press, Cambridge 1991, ISBN 0-521-40605-6.
Stanley R. Pliska: Introduction to Mathematical Finance, Discrete Time Models, Blackwell Publishers Inc., Malden (USA) and Oxford (UK), 1997, ISBN 1-557-86945-6.
Damien Lamberton and Bernard Lapeyre: Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall, London, 1996, ISBN 0-412-71800-6.
Hans Föllmer and Alexander Schied: Stochastic Finance, An Introduction in Discrete Time, De Gruyter Studies in Mathematics 27, De Gruyter 2002, ISBN 3-11-017119-8

Links to: Courses and Seminars, Finance and Insurance, RiskLab, MAS Finance

Please send comments and suggestions to Uwe Schmock, email: schmock@math.ethz.ch.
Last update: February 12, 2003.