Antonis Papapantoleon
Menu:
3236 L 374 Mathematical Finance
The Black-Scholes model implies that financial markets are complete and all risk can be hedged by trading in the underlying asset and the risk-free rate. However, the reality is completely different: markets are usually incomplete and risk cannot be hedged perfectly. The aim of this seminar is to provide a comprehensive understanding of hedging in incomplete financial markets. We wish to study different hedging criteria, e.g. mean variance, utility-indifference, or semi-static hedging, for market models driven by Lévy processes or in stochastic volatility models.The seminar will be based on the book:
- T. Rheinländer, J. Sexton: Hedging Derivatives, World Scientific, 2011.
Calendar, Speakers and Topics
- 24.10.13 – Papapantoleon: Stochastic Calculus (Chapter 2)
- 07.11.13 – Saplaouras: Arbitrage and Completeness (Chapter 3)
- 21.11.13 – Grandon: Lévy Processes (Chapter 4, § 4.1)
- 21.11.13 – Schroller: Stochastic Volatility Models (Chapter 4, § 4.2)
- 05.12.13 – Azhar: Duality Principle in Pricing (Chapter 5, § 5.1, 5.2)
- 05.12.13 – Novakova: Duality Principle in Hedging (Chapter 5, § 5.3)
- 19.12.13 – Zeidi: Fourier Methods for Pricing, Mean-Variance hedging (Chapter 6)
- 16.01.14 – Al Zoukra: Minimal Entropy Martingale Measure (Chapter 7, § 7.1, 7.2)
- 16.01.14 – Din: Entropic Valuation and Hedging (Chapter 7, § 7.3–7.5)
- 30.01.14 – Sidy: Martingale optimality principle (Chapter 8, § 8.1–8.3)
- 30.01.14 – Christodoulou: Hedging Constraints & BSDEs (Chapter 8, § 8.3–8.5)
- 13.02.14 – Besslich: Optimal Martingale Measures I (Chapter 9, § 9.1, 9.2)
- 13.02.14 – Gerdes: Optimal Martingale Measures II (Chapter 9, § 9.3–9.5)
- 20.02.14 – Papke: Efficient Hedging
- 20.02.14 – Bendrick: Mean-Variance Hedging & Applications (Chapter 6, § 6.4, 6.5)
- 20.02.14 – Eder: Dynamic utility indifference valuation (Chapter 8, § 8.6)
- A. Papapantoleon: An introduction to Lévy processes with applications in finance. Lecture notes, TU Vienna, 2008.
- A. Cox, D. Hobson: Local martingales, bubbles and option prices. Finance and Stochastics 9, 477–492, 2005.
- E. Eberlein, A. Papapantoleon, A. N. Shiryaev: On the duality principle in option pricing: semimartingale setting. Finance and Stochastics 12, 265–292, 2008.
- T. Rheinländer, M. Schmutz: Quasi self-dual exponential Lévy processes. Preprint, arXiv:1201.5132, 2012.
- E. Eberlein, K. Glau, A. Papapantoleon: Analysis of Fourier transform valuation formulas and applications. Applied Mathematical Finance 17, 211–240, 2010.
- F. Hubalek, L. Krawczyk, J. Kallsen: Variance-optimal hedging for processes with stationary independent increments. Annals of Applied Probability 16, 853–885, 2006
- M. Frittelli: The minimal entropy martingale measure and the valuation problem in incomplete markets. Mathematical Finance 10, 39–52, 2000.
- F. Delbaen, P. Grandits, T. Rheinländer, D. Samperi, M. Schweizer, C. Stricker: Exponential hedging and entropic penalties. Mathematical Finance 12, 99–123, 2002.
- F. Hubalek, C. Sgarra: Esscher transforms and the minimal entropy martingale measure for exponential Lévy models. Quantitative Finance 6, 125–145, 2006.
- M. Jeanblanc, S. Klöppel, Y. Miyahara: Minimal f^q-martingale measures for exponential Lévy processes. Annals of Applied Probability 17, 1615–1638, 2007.
- H. Föllmer, P. Leukert: Efficient hedging: Cost versus shortfall risk. Finance and Stochastics 4, 117–146, 2000.
- F. Biagini, T. Rheinländer, J. Widenmann: Hedging mortality claims with longevity bonds. ASTIN Bulletin 43, 123–157, 2013.
- M. Mania, M. Schweizer: Dynamic exponential utility indifference valuation. Annals of Applied Probability 15, 2113–2143, 2005.