Analytical approximation to constant maturity swap convexity corrections in a multi-factor SABR model

Bin Chen*, Cornelis W. Oosterlee, Sacha Van Weeren

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We consider the convexity correction in a multi-factor SABR type stochastic volatility model, in which the volatility and the short-term forward rate are modeled as independent factors. In general, the convexity correction is not analytically tractable in a multi-factor model, but based on the assumption of linear swap rates an analytic solution is available. Linear swap rate models are popular among practitioners for their efficiency and their ability to capture the swaption volatility smile. For an efficient approximation of the solution, we adopt the small disturbance asymptotics technique and construct a stochastic Taylor series of the underlying process. Several numerical experiments compare the accuracy of the approximation with a Monte Carlo benchmark solution.

Original languageEnglish
Pages (from-to)1019-1046
Number of pages28
JournalInternational Journal of Theoretical and Applied Finance
Volume13
Issue number7
DOIs
Publication statusPublished - Nov 2010

Bibliographical note

Funding Information:
We are grateful to the anonymous referees, symposium participants at the eighth European Conference on Numerical Mathematics and Advanced Applications at Uppsala (Sweden). We thank Rabobank for providing the yield curve data, Natalia Borovykh for clarifying CMS pricing practices. We also thank the members of Derivative Research & Validation team of Rabobank, Lech Grzelek, Tim Dijkstra, Giampietro Carpentieri, Floris Naber and Herwald Naaktgeboren, for their enlightening comments and suggestions. We assume full responsibility for remaining errors. We acknowledge the generous financial support of Derivative Research & Validation team of Rabobank International.

Funding

We are grateful to the anonymous referees, symposium participants at the eighth European Conference on Numerical Mathematics and Advanced Applications at Uppsala (Sweden). We thank Rabobank for providing the yield curve data, Natalia Borovykh for clarifying CMS pricing practices. We also thank the members of Derivative Research & Validation team of Rabobank, Lech Grzelek, Tim Dijkstra, Giampietro Carpentieri, Floris Naber and Herwald Naaktgeboren, for their enlightening comments and suggestions. We assume full responsibility for remaining errors. We acknowledge the generous financial support of Derivative Research & Validation team of Rabobank International.

Keywords

  • Convexity correction
  • SABR model
  • stochastic Taylor expansion

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