105.057 Mathematical Finance 2: Continuous-Time Models
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2022S, VO, 4.0h, 6.0EC
TUWEL

Properties

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

Learning outcomes

After successful completion of the course, students are able to...

  • to valuate and hedge derivatives in complete markets
  • to apply Levy- as well as stochastic volatility models
  • to appy mean-variance hedging and utility indifference valuation
  • to discuss crypto currencies

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), packets of European call and put 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, American options in the Black-Scholes-Samuelson model, trading and consumption strategies, Snell envelope, optimal stopping times, perpetual American option, exotic options (digital options, barrier options, lookback options, Asian options, basket options, quantil options), stochastic volatility, models with jumps, utility indifference pricing, mean-variance hedging, crypto currencies

Teaching methods

Blackboard presentations

Mode of examination

Oral

Lecturers

Institute

Course dates

DayTimeDateLocationDescription
Tue14:00 - 16:0001.03.2022 - 28.06.2022FH Hörsaal 3 - MATH Siehe TUWEL-Kurs
Thu14:00 - 16:0010.03.2022 - 30.06.2022FH Hörsaal 4 Siehe TUWEL-Kurs
Mathematical Finance 2: Continuous-Time Models - Single appointments
DayDateTimeLocationDescription
Tue01.03.202214:00 - 16:00FH Hörsaal 3 - MATH Siehe TUWEL-Kurs
Tue08.03.202214:00 - 16:00FH Hörsaal 3 - MATH Siehe TUWEL-Kurs
Thu10.03.202214:00 - 16:00FH Hörsaal 4 Siehe TUWEL-Kurs
Tue15.03.202214:00 - 16:00FH Hörsaal 3 - MATH Siehe TUWEL-Kurs
Thu17.03.202214:00 - 16:00FH Hörsaal 4 Siehe TUWEL-Kurs
Tue22.03.202214:00 - 16:00FH Hörsaal 3 - MATH Siehe TUWEL-Kurs
Thu24.03.202214:00 - 16:00FH Hörsaal 4 Siehe TUWEL-Kurs
Tue29.03.202214:00 - 16:00FH Hörsaal 3 - MATH Siehe TUWEL-Kurs
Thu31.03.202214:00 - 16:00FH Hörsaal 4 Siehe TUWEL-Kurs
Tue05.04.202214:00 - 16:00FH Hörsaal 3 - MATH Siehe TUWEL-Kurs
Thu07.04.202214:00 - 16:00FH Hörsaal 4 Siehe TUWEL-Kurs
Tue26.04.202214:00 - 16:00FH Hörsaal 3 - MATH Siehe TUWEL-Kurs
Thu28.04.202214:00 - 16:00FH Hörsaal 4 Siehe TUWEL-Kurs
Tue03.05.202214:00 - 16:00FH Hörsaal 3 - MATH Siehe TUWEL-Kurs
Thu05.05.202214:00 - 16:00FH Hörsaal 4 Siehe TUWEL-Kurs
Tue10.05.202214:00 - 16:00FH Hörsaal 3 - MATH Siehe TUWEL-Kurs
Thu12.05.202214:00 - 16:00FH Hörsaal 4 Siehe TUWEL-Kurs
Tue17.05.202214:00 - 16:00FH Hörsaal 3 - MATH Siehe TUWEL-Kurs
Thu19.05.202214:00 - 16:00FH Hörsaal 4 Siehe TUWEL-Kurs
Tue24.05.202214:00 - 16:00FH Hörsaal 3 - MATH Siehe TUWEL-Kurs

Examination modalities

Oral exam

Course registration

Begin End Deregistration end
01.01.2022 00:00 31.03.2022 23:59 31.03.2022 23:59

Curricula

Literature

  • Thorsten Rheinländer, Jenny Sexton: Hedging Derivatives, World Scientific, 2011, ISBN 978-9814338790, DOI: 10.1142/9789814338806.
  • 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.
  • Marek Musiela, Marek Rutkowski: Martingale Methods in Financial Modelling. Springer, 2nd ed., 2005, ISBN 3-54020-966-2.
  • 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.

Preceding courses

Accompanying courses

Language

if required in English