Real-Time Derivative Pricing and Hedging with Consistent Metamodels.

The article focuses on developing kriging-based metamodeling methods to construct consistent surfaces of derivative prices and their Greeks—sensitivities of prices to market factors—for real-time derivative pricing and hedging. It establishes the theoretical importance of consistency between price and Greek surfaces in improving hedging quality and reducing hedging costs, demonstrating that gradient-enhanced stochastic kriging (GESK) naturally ensures such consistency and yields more accurate predictions than separate stochastic kriging (SK) models. Furthermore, the study integrates partial differential equation (PDE) constraints, derived from the Feynman-Kac formula, into the GESK framework (PDE-GESK) to further enhance accuracy. Numerical experiments on various derivative types and portfolios validate that GESK and PDE-GESK outperform separate SK in accuracy and hedging performance, supporting their practical applicability in financial risk management.