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
Date Written: April 26, 2013
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: Suggested Citation