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Risks 2019, 7(1), 30; https://doi.org/10.3390/risks7010030

Model-Free Stochastic Collocation for an Arbitrage-Free Implied Volatility, Part II

1
Delft Institute of Applied Mathematics, TU Delft, 2628 XE Delft, The Netherlands
2
CWI-Centrum Wiskunde & Informatica, 1098 XE Amsterdam, The Netherlands
*
Author to whom correspondence should be addressed.
Received: 22 January 2019 / Revised: 18 February 2019 / Accepted: 20 February 2019 / Published: 6 March 2019
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Abstract

This paper explores the stochastic collocation technique, applied on a monotonic spline, as an arbitrage-free and model-free interpolation of implied volatilities. We explore various spline formulations, including B-spline representations. We explain how to calibrate the different representations against market option prices, detail how to smooth out the market quotes, and choose a proper initial guess. The technique is then applied to concrete market options and the stability of the different approaches is analyzed. Finally, we consider a challenging example where convex spline interpolations lead to oscillations in the implied volatility and compare the spline collocation results with those obtained through arbitrage-free interpolation technique of Andreasen and Huge. View Full-Text
Keywords: stochastic collocation; implied volatility; quantitative finance; arbitrage-free; risk neutral density; B-spline stochastic collocation; implied volatility; quantitative finance; arbitrage-free; risk neutral density; B-spline
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Le Floc’h, F.; Oosterlee, C.W. Model-Free Stochastic Collocation for an Arbitrage-Free Implied Volatility, Part II. Risks 2019, 7, 30.

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