Model-free stochastic collocation for an arbitrage-free implied volatility

Part I

Journal article (2019)

Authors

F.L.Y. Le Floch Numerical Analysis - EEMCS
C.W. Oosterlee Numerical Analysis - EEMCS , Centrum Wiskunde & Informatica (CWI)
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2019 F.L.Y. Le Floch, C.W. Oosterlee
DOI
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https://doi.org/10.1007/s10203-019-00238-x
Implied volatility Stochastic collocation Arbitrage-free Quantitative finance Risk-neutral density
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Published Date

01-12-2019

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

This paper explains how to calibrate a stochastic collocation polynomial against market option prices directly. The method is first applied to the interpolation of short-maturity equity option prices in a fully arbitrage-free manner and then to the joint calibration of the constant maturity swap convexity adjustments with the interest rate swaptions smile. To conclude, we explore some limitations of the stochastic collocation technique.