Call option price function in Bernstein polynomial basis with no-arbitrage inequality constraints

Journal of Inequalities and Applications

Table 1 Root mean square error (RMSE), mean absolute error (MAE), and percentage relative mean error (PRME) of the estimated call option price function (Price) and the implied volatility function (IV) with respect to mid price quotes by the proposed Bernstein polynomial method (BP) and the cubic spline smoothing method (CS)

Time to maturity in days		RMSE		MAE		PRME
Time to maturity in days		BP	CS	BP	CS	BP	CS
30	Price	0.0610	0.0427	0.0472	0.0237	−0.6694	−1.0065
30	IV	0.0017	0.0016	0.0011	0.0008	−0.0632	−0.0891
80	Price	0.1008	0.0713	0.0635	0.0406	−0.0465	−0.0477
80	IV	0.0010	0.0007	0.0007	0.0004	−0.0020	−0.0048

Results are reported for both of the times to maturity \(\tau= 30~\mbox{days}\) and \(\tau= 80~\mbox{days}\).