Pricing bermudan option via evolutionary Discrete Morse Flow approach

Bermudan option is an option that allows its holder to make an early exercise as in American option. It differs from American option in only one characteristic. Bermudan option restricts the early exercise facility to a finite number that have been specified in the contract. This option combines a characteristic from American option and European option. Therefore, its value is never greater than American option and never less than standard European option value. In this work, Bermudan option is calculated by adapting the Black-Scholes PDE, then through the numerical method called DMF (Discrete Morse Flow) the solution is determined. DMF method is a variation method, which work on time-dependent problems by discretizing time and defining a sequence of solutions that minimize the functional at every time-step. In this problem, the sequence of minimizers approach the option´s value by using evolutionary algorithm, which is Genetic algorithm. The numerical result performs also the convergence of early exercise boundary for Bermudan option to American type.