Real-Time Derivative Pricing and Hedging with Consistent Metamodels

In derivative pricing and hedging, the consistency between the price and Greek surfaces (i.e., the Greek surfaces can be obtained by differentiating the price surface) is important in stabilizing the balance sheet and reducing the hedging cost. To build consistent surfaces of the price and Greeks for real-time decisions, we propose to use the gradient -enhanced stochastic kriging method, based on the data collected through extensive simulation experiments conducted when the market is closed. In addition to the naturally guaranteed consistency, we prove that the constructed price and Greek surfaces are more accurate than those constructed separately using stochastic kriging. Besides the consistency between the price and Greeks, we show that the partial differential equation relation between the price and Greeks, implied by the famous Feynman-Kac formula, can also be used to further improve the accuracy of the constructed surfaces. The numerical studies show that our proposed metamodeling methods work well for derivative pricing and hedging.