Mathematical Finance I, Winter 2001/02
Lecturer:
Dr. Uwe Schmock
Location:
University of Zürich
,
Irchel
,
room 36 M 08
Time:
Thursday 9.15 - 12.00
First lecture:
November 1, 2001, 9.15h
Language:
German
Continuation:
Mathematical Finance II, Summer 2002
Contents:
This course treats discrete-time models. Topics are:
Review of probabilistic notation (probability spaces; product spaces; physical, subjective and synthetic probability measures; filtrations; trees; atoms; transition probabilities)
Definition of adapted and predictable stochastic processes
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
Conditional expectations (definition and basic properties)
Martingales, submartingales, supermartingales (definition and basic properties)
Stopping times and their sigma-algebras
Bayes' formula in connection with conditional expectations
Equivalent martingale measures (with bounded density)
Theorem of Dalang, Morton and Willinger (including proof in the general case)
Minimal and maximal prices of contingent claims
Markov processes (definition)
Existence of martingale measures preserving the Markov property
Call and put options in the binomial model
Digression on weak convergence
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, Snell envelopes
Forward contracts, hedge
Futures and their relation to forwards
Fixed income securities (zero-coupon bonds, bonds and their decomposition, fixed and floating rate loans)
Interest rate caps and floors, decomposition into captions and floorlets
Interest rate swaps, swap rate, hedge
Swaptions
Mathematical Finance II, Summer 2002
Lecturer:
PD Dr. Uwe Schmock
Location:
University of Zürich
,
Irchel
,
room 36 M 08
Time:
Tuesday 9.15 - 12.00
First lecture:
April 2, 2001
Language:
German
Contents:
This course treats continuous-time models. Topics are:
Filtrations, stochastic processes and stopping times
Martingales and their properties
Brownian motion and its properties
Brownian motion with drift, distribution of certain hitting times
Introduction to stochastic integration
Itô's lemma, Girsanov-Maruyama theorem
Stochastic differential equations
Black-Scholes option-pricing theory
European and American options
Please send comments and suggestions to
Uwe Schmock
, email:
schmock@fam.tuwien.ac.at
. Last update: June 14, 2003