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Analysis of Fourier transform valuation formulas and applications

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Author Info
Ernst Eberlein
Kathrin Glau
Antonis Papapantoleon
Abstract

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models.

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File URL: http://arxiv.org/abs/0809.3405
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0809.3405.

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Date of creation: Sep 2008
Date of revision: Sep 2009
Handle: RePEc:arx:papers:0809.3405

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Biagini, Francesca & Bregman, Yuliya & Meyer-Brandis, Thilo, 2008. "Pricing of catastrophe insurance options written on a loss index with reestimation," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 214-222, October. [Downloadable!] (restricted)
  2. Martin Keller-Ressel & Antonis Papapantoleon & Josef Teichmann, 2009. "A new approach to LIBOR modeling," Quantitative Finance Papers 0904.0555, arXiv.org. [Downloadable!]
  3. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal Of The Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241. [Downloadable!] (restricted)
  4. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Quantitative Finance Papers math/0607112, arXiv.org. [Downloadable!]
  5. Ernst Eberlein & Antonis Papapantoleon & Albert N. Shiryaev, 2008. "Esscher transform and the duality principle for multidimensional semimartingales," Quantitative Finance Papers 0809.0301, arXiv.org, revised Nov 2009. [Downloadable!]
  6. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," Journal of Business, University of Chicago Press, vol. 63(4), pages 511-24, October. [Downloadable!] (restricted)
  7. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412. [Downloadable!] (restricted)
  8. T. R. Hurd & Zhuowei Zhou, 2009. "A Fourier transform method for spread option pricing," Quantitative Finance Papers 0902.3643, arXiv.org. [Downloadable!]
  9. Ernst Eberlein & Antonis Papapantoleon & Albert Shiryaev, 2008. "On the duality principle in option pricing: semimartingale setting," Finance and Stochastics, Springer, vol. 12(2), pages 265-292, April. [Downloadable!] (restricted)
  10. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April. [Downloadable!]
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  1. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2009. "Analyticity of the Wiener-Hopf factors and valuation of exotic options in L\'evy models," Quantitative Finance Papers 0911.0373, arXiv.org. [Downloadable!]
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