Abstract
In incomplete markets, a basic Black-Scholes perspective has to be complemented by the valuation of market imperfections. Otherwise this results in Black-Scholes Ponzi schemes, such as the ones at the core of the last global financial crisis, where always more derivatives need to be issued for remunerating the capital attracted by the already opened positions. In this paper we consider the sustainable Black-Scholes equations that arise for a portfolio of options if one adds to their trade additive Black-Scholes price, on top of a nonlinear funding cost, the cost of remunerating at a hurdle rate the residual risk left by imperfect hedging. We assess the impact of model uncertainty in this setup.
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Acknowledgements
The research of Stéphane Crépey benefited from the support of the “Chair Markets in Transition”, Fédération Bancaire Française, of the ANR project 11-LABX-0019 and of the EIF grant “Collateral management in centrally cleared trading”. The travel expenses of Stéphane Crépey regarding its participation to the ICASQF 2016 conference were funded by l’Institut Français de Colombie, Carrera 11 No. 93–12, Ambassade de France en Colombie. The research of Chao Zhou is supported by NUS Grants R-146-000-179-133 and R-146-000-219-112.
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Armenti, Y., Crépey, S., Zhou, C. (2017). The Sustainable Black-Scholes Equations. In: Londoño, J., Garrido, J., Jeanblanc, M. (eds) Actuarial Sciences and Quantitative Finance. ICASQF 2016. Springer Proceedings in Mathematics & Statistics, vol 214. Springer, Cham. https://doi.org/10.1007/978-3-319-66536-8_8
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DOI: https://doi.org/10.1007/978-3-319-66536-8_8
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