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

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

Blackboard presentations

Oral exam

• 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.