Jorge Zubelli  (Khalifa University, UAE &  ADIA Lab, UAE)

Title:  Calibration of Jump-Diffusion Models with Local Volatility from Derivative Prices

We focus on the calibration of Dupire's local volatility model in the presence of jumps. Dupire's model is extensively used for hedging and option pricing in financial markets.

Given the ill-posed nature of local volatility surface calibration from market prices, we employ regularization techniques. More precisely, we use convex regularization tools and recent advances in inverse problems to tackle this challenge. Our approach involves using a forward Dupire-type partial-integro-differential equation for option prices to compute the parameter-to-solution map. We then solve the ill-posed inverse problem using a Tikhonov-type convex regularization.

We present numerical examples to demonstrate the robustness of our method for both synthetic and real data. This work is a collaboration with Vinicius Albani (UFSC).