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

Matthias Fengler & Lin-Yee Hin

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abstract We suggest a semi-nonparametric estimator for the call-option price surface. The estimator is a bivariate tensor-product B-spline. To enforce no-arbitrage constraints across strikes and expiry dates, we establish sufficient no-arbitrage conditions on the control net of the B-spline surface. The conditions are linear and therefore allow for an implementation of the estimator by means of standard quadratic programming techniques. The consistency of the estimator is proved. By means of simulations, we explore the statistical efficiency benefits that are associated with estimating option price surfaces and state-price densities under the full set of no-arbitrage constraints. We estimate a call-option price surface, families of first-order strike derivatives, and state-price densities for S&P 500 option data.
   
type journal paper
   
keywords option pricing function, implied volatility, no-arbitrage constraints, state price density, semi-nonparametric estimation, B-splines
   
language English
kind of paper journal article
date of appearance 2-9-2015
journal Journal of Econometrics
publisher Elsevier (Amsterdam)
ISSN 0304-4076
ISSN (online) 1872-6895
DOI 10.1016/j.jeconom.2014.09.003
volume of journal 184
number of issue 2
page(s) 242-261
review double-blind review
   
profile area SEPS - Quantitative Economic Methods
citation Fengler, M., & Hin, L. Y. (2015). Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints. Journal of Econometrics, 184(2), 242-261, DOI:10.1016/j.jeconom.2014.09.003.