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Semi-Nonparametric Estimation of the Call Price Surface Under Strike and Time-to-expiry No-Arbitrage Constraints

54 Pages Posted: 17 Aug 2011 Last revised: 19 Mar 2015

Matthias R. Fengler

University of St. Gallen - School of Economics and Political Science

Lin-Yee Hin

Department of Mathematics & Statistics, Curtin University

Date Written: April 26, 2013

Abstract

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.

Keywords: option pricing function, implied volatility, no-arbitrage constraints, state price density, local volatility, semi-nonparametric estimation, B-splines

JEL Classification: C14, C58, G13

Suggested Citation

Fengler, Matthias R. and Hin, Lin-Yee, Semi-Nonparametric Estimation of the Call Price Surface Under Strike and Time-to-expiry No-Arbitrage Constraints (April 26, 2013). Journal of Econometrics, No. 184, 2015, pp. 242-261. Available at SSRN: https://ssrn.com/abstract=1910737 or http://dx.doi.org/10.2139/ssrn.1910737

Matthias R. Fengler (Contact Author)

University of St. Gallen - School of Economics and Political Science ( email )

Bodanstrasse 6
CH-9000 St. Gallen, 9000
Switzerland

HOME PAGE: http://www.mathstat.unisg.ch/fengler

Lin-Yee Hin

Department of Mathematics & Statistics, Curtin University ( email )

Kent Street
Bentley
Perth
Australia

HOME PAGE: http://hk.linkedin.com/in/linyeehin

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