This paper discusses computational consequences of the insight of Schröder (1999) that the pricing of double-barrier options is determined by modular forms. The numerical properties of one of the valuation series of Schröder (1999), together with the corresponding estimate of its convergence rate, are studied in comparison with the Kunitomo-Ikeda valuation series. These numerical properties are determined by the convergence parameter. This new notion depends on the volatility of the underlying, the option's time to maturity, and the logarithms of the upper and lower barrier of the option. The smaller this convergence parameter, the faster is the convergence of pricing series of the Kunitomo-Ikeda type. Analogous results are shown to hold for delta hedging and are illustrated in situations "near the barrier".