Option pricing model under the G-expectation framework
This provides a robust valuation method for financial markets under uncertainty, but it is incremental as it builds on existing G-expectation theory.
The paper tackled robust option pricing under model uncertainty by developing a G-Black-Scholes equation within the G-expectation framework, and introduced logarithmic transformation and finite difference schemes that achieved high accuracy and improved computational efficiency.
G-expectation, as a sublinear expectation, provides a powerful framework for modeling uncertainty in financial markets. Motivated by the need for robust valuation under model uncertainty, this work develops a unified risk-neutral valuation approach within the G-expectation environment, yielding a nonlinear generalization of the Black-Scholes model, termed the G-Black-Scholes equation. To enhance computational efficiency and reduce numerical cost, we introduce a logarithmic transformation of the asset price, which yields an alternative nonlinear PDE. Based on this transformed formulation, we design both explicit and implicit finite difference schemes that are rigorously demonstrated to be consistent, stable, monotone, and convergent to the viscosity solution. Numerical examples confirm that the proposed schemes achieve high accuracy, while the logarithmic transformation relaxes the stability constraints of explicit schemes and improves computational efficiency.