Robustness of quadratic hedging strategies in finance via Fourier transforms

In this paper we investigate the consequences of the choice of the model to partial hedging in incomplete markets in finance. In fact we consider two models for the stock price process. The first model is a geometric Lévy process in which the small jumps might have infinite activity. The second mode...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2016-04, Vol.296, p.56-88
Main Authors: Daveloose, Catherine, Khedher, Asma, Vanmaele, Michèle
Format: Article
Language:English
Subjects:
Brownian motion
Convergence
Finance
Fourier transforms
Lévy processes
Mathematical models
Options
Quadratic hedging
Raw materials
Robustness
Strategy
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Summary:In this paper we investigate the consequences of the choice of the model to partial hedging in incomplete markets in finance. In fact we consider two models for the stock price process. The first model is a geometric Lévy process in which the small jumps might have infinite activity. The second model is a geometric Lévy process where the small jumps are truncated or replaced by a Brownian motion which is appropriately scaled. To prove the robustness of the quadratic hedging strategies we use pricing and hedging formulas based on Fourier transform techniques. We compute convergence rates and motivate the applicability of our results with examples.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.09.005