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Erscheinungsjahr: 
2019
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[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 7 [Issue:] 1 [Article No.:] 30 [Publisher:] MDPI [Place:] Basel [Year:] 2019 [Pages:] 1-21
Verlag: 
MDPI, Basel
Zusammenfassung: 
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.
Schlagwörter: 
stochastic collocation
implied volatility
quantitative finance
arbitrage-free
risk neutral density
B-spline
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