A method and computer apparatus determines the value of a derivative by introducing risk premiums. The method includes determining the underlying security and derivative, determining the risks and trading costs associated with the derivative, formulating the RAP equation for the derivative, solving the RAP equation for the derivative and outputting a value of the derivative based on the solution of the RAP equation. The computer apparatus employs this method in a financial analysis application. The system includes an input unit for taking inputs of derivative characteristics and model parameters, a processing unit for computing a value of the derivative based on the input characteristics and parameters using a risk-adjusted pricing equation, and an output unit for displaying the value of the derivative.