Preprint serie E55/2018
A Splitting Strategy for the Calibration of Jump-Diffusion Models
Vinicius Albani, Jorge Zubelli
Keywords: quantitative finance, jump-diffusion processes, local volatility, Inverse Problems

We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local-volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion driven asset with time and price dependent volatility.
Our approach uses a forward Dupire-type partial-integro-differential equations for the option prices to produce a parameter-to-solution map. The ill-posed inverse problem for such map is then solved by means of a Tikhonov-type convex regularization. The proofs of convergence and stability of the algorithm are provided together with numerical examples that substantiate the robustness of the method both for synthetic and real data.

MSC 2000: 91G20