American Put Option: Richardson's extrapolation and a Posteriori Error Estimator for a Front-Fixing Finite Difference Scheme

In the market for financial derivatives, the most important problem is the so-called {it option valuation problem} or in a few words: the problem of computing a fair price for a given option. Analytical solutions of American options problems are seldom available, but such derivatives of financial markets can be priced by numerical methods. For the numerical solution of the American option valuation problem, we provide a script written in MATLAB implementing an explicit finite difference scheme. Our main contribute is the definition of a posteriori error estimator for the American options pricing which is based on Richardson's extrapolation theory. This error estimator allows us to find a suitable grid where the computed solution, both the option price field variable and the free boundary position, verify a prefixed error tolerance.