Abstract
We discuss the difference between locally risk-minimizing and delta hedging strategies for exponential Lévy models, where delta hedging strategies in this paper are defined under the minimal martingale measure. We give firstly model-independent upper estimations for the difference. In addition we show numerical examples for two typical exponential Lévy models: Merton models and variance gamma models.
References
Arai, T., Imai, Y., Suzuki, R.: Numerical local risk minimization for exponential Lévy models. Int. J. Theor. Appl. Finan. 19, 1650008 (2016)
Arai, T., Suzuki, R.: Local risk-minimization for Lévy markets. Int. J. Finan. Eng. 02, 1550015 (2015)
Carr, P., Madan, D.: Option valuation using the fast Fourier transform. J. Comput. Finan. 2, 61–73 (1999)
Denkl, S., Goy, M., Kallsen, J., Muhle-Karbe, J., Pauwels, A.: On the performance of delta hedging strategies in exponential Lévy models. Quant. Finan. 13, 1173–1184 (2013)
Imai, Y., Arai, T.: Comparison of local risk minimization and delta hedging for exponential Lévy models. JSIAM Lett. 7, 77–80 (2015)
Schweizer, M.: A Guided Tour through Quadratic Hedging Approaches, Handbooks in Mathematical Finance: Option Pricing, Interest Rates and Risk Management, pp. 538–574. Cambridge University Press, Cambridge (2001)
Schweizer, M.: Local risk-minimization for multidimensional assets and payment streams. Banach Cent. Publ. 83, 213–229 (2008)
Solé, J.L., Utzet, F., Vives, J.: Canonical Lévy process and Malliavin calculus. Stoch. Proc. Appl. 117, 165–187 (2007)
Acknowledgements
Takuji Arai was supported by JSPS Grant-in-Aid for Scientific Research (C) No.15K04936. Yuto Imai was supported by JSPS Grant-in-Aid for Young Scientists (B) No. 17K13764 and Waseda University Grants for Special Research Projects (Project Number: 2016K-174 and 2016B-123).
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Arai, T., Imai, Y. On the difference between locally risk-minimizing and delta hedging strategies for exponential Lévy models. Japan J. Indust. Appl. Math. 34, 845–858 (2017). https://doi.org/10.1007/s13160-017-0268-6
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DOI: https://doi.org/10.1007/s13160-017-0268-6