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