Recovering the Time-Dependent Volatility in Jump-Diffusion Models from Nonlocal Price Observations

This paper is devoted to a recovery of time-dependent volatility under jump-diffusion processes assumption. The problem is formulated as an inverse problem: given nonlocal observations of European option prices, find a time-dependent volatility function such that the theoretical option prices match the observed ones in an optimal way with respect to a prescribed cost functional. We propose a variational adjoint equation approach to derive the gradients of the functionals. A finite difference formulation of the 1D inverse problem is discussed.