Model-Free Stochastic Collocation for an Arbitrage-Free Implied Volatility, Part II
by
Fabien Le Floc’h 1,* and
Cornelis W. Oosterlee 1,2
Fabien Le Floc’h 1,* and
Cornelis W. Oosterlee 1,2
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.
Risks 2019, 7(1), 30; https://doi.org/10.3390/risks7010030
Received: 22 January 2019 / Revised: 18 February 2019 / Accepted: 20 February 2019 / Published: 6 March 2019
(This article belongs to the Special Issue Modern Numerical Techniques and Machine-Learning in Pricing and Risk Management)
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.
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Keywords:
stochastic collocation; implied volatility; quantitative finance; arbitrage-free; risk neutral density; B-spline
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MDPI and ACS Style
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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