A data processing apparatus and method are provided for calculating an implied correlation and/or dispersion of an index that has a plurality of constituents. Data is received which describes properties of the index and properties of at least some of its constituents. An implied variance of the index and an implied variance of each of the at least some constituents are determined based on the received data. The implied correlation and/or dispersion of the index are calculated using the determined implied variances. A variance calculation scheme may be used which does not require the calculation of a volatility. Further, a model-free algorithm may be used to determine the implied valiances. Furthermore, an implied volatility of the index and an implied volatility for constituents may be determined from the implied variances.