Calibration the drift term of Jump-Diffusion Option Pricing Model

The book introduces a finance calibration issue, aiming to determine model parameters using observed option prices. It delves into using intricate models like multi-dimensional jump diffusion with stochastic volatility to price European and Quanto options. Several numerical techniques-integro-differential stochastic equations, finite elements, Monte Carlo, and Quasi Monte Carlo methods-are examined for pricing. The Tikhonov regularization method is proposed to solve the calibration problem by converting it into an inverse problem of partial differential equations, solvable via numerical methods. Additionally, it explores the role of the optimal control framework in establishing conditions to minimize cost functionals. Despite the challenges in estimation, the model displays promise in calibration, exhibiting accuracy in theoretical outcomes and numerical experiments, demonstrating potential risk reduction capabilities.