Department of Mathematics

Pricing and Hedging with Jump Processes

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Organizers Johannes Muhle-Karbe, Marcel Nutz, Martin Schweizer
Place HG G 5
Time We 08:15-10:00
Beginning 06.10.2010
Contact Johannes Muhle-Karbe, Marcel Nutz
Prerequisites solid knowledge of mathematical finance and stochastic processes
Description We study the pricing and hedging of options in models where asset prices are modeled by Lévy processes. Since these incorporate jumps, the resulting markets are incomplete such that the methodology of pricing and hedging by replication is not applicable. We will discuss several alternatives, including calibration to market prices, super-replication, mean-variance hedging and approaches based on utility maximization.
Literature NOTE: You may need to use an IP address from ETH (computer at ETH or via VPN) to access the papers.

[1] Cont, R. and Voltchkova, E. (2005): Integro-differential equations for option prices in exponential Lévy models. Finance and Stochastics, 9(3) 299-325. Link

[2] Carr, P. and Madan, D. (1999): Option Pricing and the Fast Fourier Transform.  Journal of Computational Finance, 2(4) 61-73. Link

[3] Cont, R. and Tankov, P. (2006): Retrieving Lévy processes from option prices: Regularization of an ill-posed inverse problem. SIAM Journal of Control and Optimization 45(1) 1-25. Link

[4] Eberlein, E. and Jacod, J. (1997): On the range of option prices. Finance and Stochastics, 1(2) 131-140. Link

[5] Cont, R., Tankov, P., and Voltchkova, E. (2007): Hedging with options in models with jumps. In "Stochastic Analysis and Applications - the Abel Symposium 2005", 197-218. Link

[6] Schweizer, M. (1994): Approximating random variables by stochastic integrals. The Annals of Probability, 22(3) 1536-1575. Link

[7] Hubalek, F., Kallsen, J., and Krawczyk, L. (2006): Variance-optimal hedging for processes with independent stationary increments. The Annals of Applied Probability, 16(2) 853-885. Link

[8] Davis, M.H.A. (1998): Option pricing in incomplete markets. In "Mathematics and Derivative Securities", 216-226. Link

[9] Karatzas, I. and Kou, S. (1996): On the pricing of contingent claims under constraints. The Annals of Applied Probability, 6(2) 321-369. Link

Registration We welcome registrations before the first meeting (email to Marcel) and may even hand out some topics on that basis. We intend to distribute most of the topics after the first meeting.
Additional information Each student is expected to give a talk about one of the above papers. Certain papers might be covered by two students. Talks are in English.

The seminar yields 6 credit points. To obtain these, students should regularly attend the seminar and give a successful talk.


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