RECOVERING PROBABILITY FUNCTIONS WITH FOURIER SERIES

. The COS method was introduced in Fang & Oosterlee (2008) and then was applied to pricing a variety of stock options for continuous random variables. This paper adapts the Fourier-cosine series (COS) method to recover discrete probability mass functions. We approximate mixture and compound probability distributions with cosine series. Enormous precision and computational speed are the qualities of the function estimates here obtained. We also develop the pricing framework to trade derivatives subject to discrete random variables. We apply the method to calculate, for the first time, the price of an interest rate derivative of recent vintage introduced in the Brazilian financial market. Parameter calibration confirms the quality of the model.