An inverse finance problem for estimating volatility in American option pricing under jump-diffusion dynamics

This study attempts to estimate the volatility of the American options pricing model under jump-diffusion underlying asset model. Therefore, the problem is formulated then inverted, and afterward, direct finance problems are defined. It is demonstrated, then, that the price of this type of options satisfies a free boundary Partial Integral Differential Equation (PIDE). The inverse method for estimating the volatility and the American options price is also described in three phases: first, transformation of the direct problem to a non-linear initial and boundary value problem. Second, finding the solution by using the method of lines and the fourth-order Runge-Kutta method.Third, presenting a minimization function with Tikhonov regularization.

کلیدواژه ها:

Emden-Fowler equations ، integral equation ، Volterra ، moving least squares method