A perturbative approach for reconstructing diffusion coefficients

摘要

In this note we present a perturbative method for obtaining the diffusion coefficient of a parabolic equation from the knowledge of a particular solution of the equation. The procedure is carried out in the context of the problem consisting of finding the volatility as a function of the strike price of the European option. We end with some numerical experiments that show the behavior of the proposed method. These examples show that even though the method yields reconstructions producing very good fit to the data, the reconstructed coefficient may be very different from the true diffusion coefficient.