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Moving Least Squares for Arbitrage-Free Price and Volatility Surfaces

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Topics in Numerical Methods for Finance

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 19))

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Abstract

To price exotic options consistently to market data, it is necessary to approximate the implied volatility surface (IVS) over the strike–maturity plane. To avoid mis-pricing and arbitrage strategies, the approximation must be arbitrage free. Based on the moving least squares (MLS) reconstruction, a numerical approach is presented in this paper to compute arbitrage-free surfaces which approximate observed market data.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität zu Köln, 86–90, Weyertal, 50937, Köln, Germany

    Pascal Heider

Authors
  1. Pascal Heider
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Correspondence to Pascal Heider .

Editor information

Editors and Affiliations

  1. , Dublin City Univ. Business School, Dublin City University, Ballymun Rd, Dublin 9, Dublin 9, Ireland

    Mark Cummins

  2. , Kemmy Business School, University of Limerick, Limerick, Ireland

    Finbarr Murphy

  3. Inst. for Numerical Computat. & Analy., 7 - 9 Dame Court, Dublin 2, Dublin 2, Ireland

    John J.H. Miller

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Heider, P. (2012). Moving Least Squares for Arbitrage-Free Price and Volatility Surfaces. In: Cummins, M., Murphy, F., Miller, J. (eds) Topics in Numerical Methods for Finance. Springer Proceedings in Mathematics & Statistics, vol 19. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-3433-7_2

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