# 105.057 Mathematical Finance 2: Continuous-Time Models This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_20",{id:"j_id_20",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_22",{id:"j_id_22",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2021S 2020S 2019S 2018S 2017S 2016S 2015S 2014S 2013S 2012S 2011S 2010S 2009S 2008S 2007S 2006S 2005S

2013S, VO, 4.0h, 6.0EC

## Properties

• Semester hours: 4.0
• Credits: 6.0
• Type: VO Lecture

## Aim of course

Introduction to mathematical finance in continuous time. Risk management of financial assets.

## Subject of course

Black-Scholes-Samuelson model (types of trading strategies, martingale measures, Black-Scholes formula, replicating strategies, Black-Scholes PDGL, call-put parity, Black-Scholes sensitivities, time-dependent coefficients), packets of European call and put options, forward-start options, chooser options, compound options, stocks with dividends, Bachelier model, forward and futures contracts, Black model, Black formulas for options on futures, cross-currency market model, domestic and foreign martingale measure, currency forward contract and options, European options on foreign equity, quanto forward contracts, foreign market futures contracts, American options in the Black-Scholes-Samuelson model, trading and consumption strategies, Doob-Meyer decomposition, Snell envelope, optimal stopping times, perpetual American option, exotic options (digital options, barrier options, lookback options, Asian options, basket options, quantil options), outlook (e.g. multi-dimensional Black-Scholes-Samuelson model, stochastic volatility, models with jumps)

## Course dates

DayTimeDateLocationDescription
Tue14:00 - 16:0005.03.2013FH Hörsaal 3 - MATH Erster Termin
Thu11:30 - 13:1507.03.2013FH Hörsaal 7 - GEO .
Tue14:30 - 16:0012.03.2013 - 18.06.2013FH Hörsaal 3 - MATH .
Thu14:30 - 16:3014.03.2013 - 20.06.2013FH Hörsaal 4 .
Tue14:00 - 14:3014.05.2013 - 18.06.2013FH Hörsaal 3 - MATH FM2: VO-Beginn 14:00 wegen Entfall einiger Termine
Thu14:00 - 14:3016.05.2013 - 20.06.2013FH Hörsaal 4 FM2: VO-Beginn 14:00 wegen Entfall einiger Termine
Mathematical Finance 2: Continuous-Time Models - Single appointments
DayDateTimeLocationDescription
Tue05.03.201314:00 - 16:00FH Hörsaal 3 - MATH Erster Termin
Thu07.03.201311:30 - 13:15FH Hörsaal 7 - GEO .
Tue12.03.201314:30 - 16:00FH Hörsaal 3 - MATH .
Thu14.03.201314:30 - 16:30FH Hörsaal 4 .
Tue19.03.201314:30 - 16:00FH Hörsaal 3 - MATH .
Thu21.03.201314:30 - 16:30FH Hörsaal 4 .
Tue09.04.201314:30 - 16:00FH Hörsaal 3 - MATH .
Thu11.04.201314:30 - 16:30FH Hörsaal 4 .
Tue16.04.201314:30 - 16:00FH Hörsaal 3 - MATH .
Thu18.04.201314:30 - 16:30FH Hörsaal 4 .
Tue23.04.201314:30 - 16:00FH Hörsaal 3 - MATH .
Thu25.04.201314:30 - 16:30FH Hörsaal 4 .
Tue30.04.201314:30 - 16:00FH Hörsaal 3 - MATH .
Thu02.05.201314:30 - 16:30FH Hörsaal 4 .
Tue07.05.201314:30 - 16:00FH Hörsaal 3 - MATH .
Tue14.05.201314:00 - 14:30FH Hörsaal 3 - MATH FM2: VO-Beginn 14:00 wegen Entfall einiger Termine
Tue14.05.201314:30 - 16:00FH Hörsaal 3 - MATH .
Thu16.05.201314:00 - 14:30FH Hörsaal 4 FM2: VO-Beginn 14:00 wegen Entfall einiger Termine
Thu16.05.201314:30 - 16:30FH Hörsaal 4 .
Thu23.05.201314:00 - 14:30FH Hörsaal 4 FM2: VO-Beginn 14:00 wegen Entfall einiger Termine

## Examination modalities

written and oral exam The written exam can be taken at one of three dates during the semester. Dates and details can be found here: http://www.fam.tuwien.ac.at/lehre/pr/index.php

Not necessary

## Literature

• Marek Musiela, Marek Rutkowski: Martingale Methods in Financial Modelling. Springer, 2nd ed., 2005, ISBN 3-54020-966-2.
• Monique Jeanblanc-Picqué, Marc Yor, Mark Chesney: Mathematical Methods for Financial Markets. Springer, 2009, ISBN 978-1-85233-376-8, DOI 10.1007/978-1-84628-737-4.
• Steven E. Shreve: Stochastic Calculus for Finance II. Continuous-Time Models. Springer, 2004, ISBN 0-38740-101-6.
• Ioannis Karatzas, Steven E. Shreve: Methods of Mathematical Finance. Springer, corr. 2. pr., 1999, ISBN 0-387-9839-2.
• Damien Lamberton, Bernard Lapeyre: Introduction to Stochastic Calculus Applied to Finance. Chapman & Hall, 2nd ed., 2008, ISBN 978-1-58488-626-6.
• Tomas Björk: Arbitrage Theory in Continuous Time. Oxford University Press, 2nd ed., 2004, ISBN 978-0-19927-126-9.
• Martin Baxter, Andrew Rennie: Financial Calculus. Cambridge University Press, 1998, ISBN 0-52155-289-3.

Foundations

• Hans Föllmer, Alexander Schied: Stochastic Finance. An Introduction in Discrete Time. De Gruyter, 3rd ed., 2011, ISBN: 978-3110218046.
• Bernt K. Øksendal: Stochastic Differential Equations, an Introduction with Applications. Springer, 6th ed., 2007, ISBN 978-3-54004-758-2.
• Daniel Revuz, Marc Yor: Continuous Martingales and Brownian Motion. Springer, 3. ed., corr. 3. print., 2005, ISBN 3-54064-325-7.
• Olav Kallenberg: Foundations of Modern Probability. Springer, 2nd ed., 2002, ISBN 0-38795-313-2.
• Ioannis Karatzas, Steven E. Shreve: Brownian Motion and Stochastic Calculus. Springer, 2. ed., corr. 6. print., 2000, ISBN 0-38797-655-8.

German