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

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

Blackboard presentations

Oral exam

• 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.