Solves the inverse problem: find the parameters which most closely appoximate the option prices available in the market. Requires specification of a characeteristic function. Some useful characteristic functions are provided in the cf_functions repository. This module works by fitting a monotonic spline to transformed option data from the market. Then the empirical characteristic function is estimated from the spline. A mean squared optimization problem is then solved in complex space between the analytical characteristic function and the empirical characteristic function. For more documentation and results, see fang_oost_cal_charts. Currently this module only works on a single maturity at atime. It does not calibrate across all maturities simultanously.
Fang Oosterlee approach for an option using the underlying's characteristic function. Some useful characteristic functions are provided in the cf_functions repository. Fang and Oosterlee's approach works well for a smaller set of discrete strike prices such as those in the market. The constraint is that the smallest and largest values in the x domain must be relatively far from the middle values. This can be "simulated" by adding small and large strikes synthetically. Due to the fact that Fang Oosterlee is able to handle discrete strikes well, the algorithm takes a vector of strike prices with no requirement that the strike prices be equidistant. All that is required is that they are sorted largest to smallest. Link to Fang-Oosterlee paper.