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.
Original language | English |
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Article number | 30 |
Journal | Risks |
Volume | 7 |
Issue number | 1 |
DOIs | |
Publication status | Published - Mar 2019 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2019 by the authors. Licensee MDPI, Basel, Switzerland.
Keywords
- Arbitrage-free
- B-spline
- Implied volatility
- Quantitative finance
- Risk neutral density
- Stochastic collocation