Model-free stochastic collocation for an arbitrage-free implied volatility: Part I

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 con...

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Bibliographic Details
Published in:Decisions in economics and finance 2019-12, Vol.42 (2), p.679-714
Main Authors: Le Floc’h, Fabien, Oosterlee, Cornelis W.
Format: Article
Language:English
Subjects:
Arbitrage
Collocation
Convexity
Econometrics
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Finance
Interpolation
Management
Maturity
Operations Research/Decision Theory
Polynomials
Prices
Pricing
Public Finance
Securities prices
Volatility
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Summary: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.
ISSN:1593-8883
1129-6569
DOI:10.1007/s10203-019-00238-x