Numerical Determination of Time-Dependent Volatility for American Option When the Optimal Exercise Boundary Is Known

The paper is devoted on developing a robust free-boundary based method for reconstruction time-dependent volatility of American put options. This problem is posed as an inverse problem: given the optimal exercise boundary, find the volatility function. We propose a linearization refereed to the semi-time layers algorithm of decomposition of the approximate solution for which the transition to the new time level is carried out by two ODE problems. The correctness of the method is discussed. We test the efficiency of the approach for synthetic and close to deal market data.