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

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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.

Original languageEnglish
Pages (from-to)679-714
Number of pages36
JournalDecisions in Economics and Finance
Volume42
Issue number2
DOIs
Publication statusPublished - 1 Dec 2019

Keywords

  • Arbitrage-free
  • Implied volatility
  • Quantitative finance
  • Risk-neutral density
  • Stochastic collocation

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