Thu, November 4, 2021, 9:00-10:00 am PDT via Zoom
Title: A Splitting Strategy for the Calibration of Jump-Diffusion Models.
Abstract: This talk concerns the calibration of Dupire’s model in the presence of jumps. This leads to an integro-differential equation whose parameters have to be calibrated so as to fit market data. 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 equation for the option prices to produce a parameter-to-solution map. The ill-posed inverse problem for such a map is then solved by means of a Tikhonov-type convex regularization. We present numerical examples that substantiate the robustness of the method both for synthetic and real data. This is joint work with Vinicius Albani (UFSC) that appeared in Finance and Stochastics.