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.

2024S, VO, 4.0h, 6.0EC

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

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, 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, stochastic volatility, models with jumps, utility indifference pricing, mean-variance hedging

Teaching methods

Blackboard presentations

Mode of examination

Oral

Lecturers

Institute

Course dates

DayTimeDateLocationDescription
Tue14:00 - 16:0005.03.2024 - 25.06.2024FH Hörsaal 3 - MATH .
Thu14:00 - 16:0007.03.2024 - 27.06.2024Sem.R. DA grün 03 B .
Mathematical Finance 2: Continuous-Time Models - Single appointments
DayDateTimeLocationDescription
Tue05.03.202414:00 - 16:00FH Hörsaal 3 - MATH .
Thu07.03.202414:00 - 16:00Sem.R. DA grün 03 B .
Tue12.03.202414:00 - 16:00FH Hörsaal 3 - MATH .
Thu14.03.202414:00 - 16:00Sem.R. DA grün 03 B .
Tue19.03.202414:00 - 16:00FH Hörsaal 3 - MATH .
Thu21.03.202414:00 - 16:00Sem.R. DA grün 03 B .
Tue09.04.202414:00 - 16:00FH Hörsaal 3 - MATH .
Thu11.04.202414:00 - 16:00Sem.R. DA grün 03 B .
Tue16.04.202414:00 - 16:00FH Hörsaal 3 - MATH .
Thu18.04.202414:00 - 16:00Sem.R. DA grün 03 B .
Tue23.04.202414:00 - 16:00FH Hörsaal 3 - MATH .
Thu25.04.202414:00 - 16:00Sem.R. DA grün 03 B .
Tue30.04.202414:00 - 16:00FH Hörsaal 3 - MATH .
Thu02.05.202414:00 - 16:00Sem.R. DA grün 03 B .
Tue07.05.202414:00 - 16:00FH Hörsaal 3 - MATH .
Tue14.05.202414:00 - 16:00FH Hörsaal 3 - MATH .
Thu16.05.202414:00 - 16:00Sem.R. DA grün 03 B .
Thu23.05.202414:00 - 16:00Sem.R. DA grün 03 B .
Tue28.05.202414:00 - 16:00FH Hörsaal 3 - MATH .
Tue04.06.202414:00 - 16:00FH Hörsaal 3 - MATH .

Examination modalities

Oral exam

Course registration

Begin End Deregistration end
06.01.2024 00:00 04.04.2024 23:59 04.04.2024 23:59

Curricula

Study CodeObligationSemesterPrecon.Info
066 405 Financial and Actuarial Mathematics Mandatory
860 GW Optional Courses - Technical Mathematics Not specified

Literature

  • Thorsten Rheinländer, Jenny Sexton: Hedging Derivatives, World Scientific, 2011, ISBN 978-9814338790, DOI: 10.1142/9789814338806.
  • Andrea Pascucci: PDE and Martingale Methods in Option Pricing, Springer 2011
  • 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