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.