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

Fabien Le Floc’h and Cornelis Oosterlee
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Fabien Le Floc’h: Delft Institute of Applied Mathematics, TU Delft, 2628 XE Delft, The Netherlands

Risks, 2019, vol. 7, issue 1, 1-21

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.

Keywords: stochastic collocation; implied volatility; quantitative finance; arbitrage-free; risk neutral density; B-spline (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Journal Article: Model-free stochastic collocation for an arbitrage-free implied volatility: Part I (2019)
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:7:y:2019:i:1:p:30-:d:211431

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