Computer-based systems and methods for calibrating a surface. The surface may be a 1-D or multi-D surface, such as a volatility grid used to price financial instruments whose price depends on volatility. The computer system may comprise: a database that stores calibration input data; a processor in communication with the database; and a memory in communication with the processor. The memory stores instructions which when executed by the processor causes the processor to calculate entries for a vector representing the surface based on the calibration input data. The entries for the vector representing the surface are calculated based on a product of a matrix of a set of basis functions and a vector of coefficients for the set of basis functions, where entries for the vector of coefficients are determined based on the calibration input data. In various implementations, the set of basis functions comprises a set of b-spline basis functions.