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Semi-nonparametric estimation of the call price surface under strike and time-to-expiry no-arbitrage constraints

  • Fengler, Matthias


  • Hin, Lin-Yee


We suggest a semi-nonparametric estimator for the entire call price surface based on a tensor-product B-spline. To enforce no-arbitrage constraints in strike and calendar dimensions we establish sufficient no-arbitrage conditions on the control net of the tensor product (TP) B-spline. Since these conditions are independent of the degrees of the underlying polynomials, the estimator can be parametrized with TP B-splines of arbitrary order. We derive consistency and explore the statistical efficiency benefits from surface estimation. As an application, we estimate families of state price densities and a local volatility surface for S&P500 option data.

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Paper provided by University of St. Gallen, School of Economics and Political Science in its series Economics Working Paper Series with number 1136.

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Length: 57 pages
Date of creation: Sep 2011
Date of revision: May 2013
Handle: RePEc:usg:econwp:2011:36
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