Pricing and hedging derivative securities with neural networks and a homogeneity hint

We estimate a generalized option pricing formula that has a functional shape similar to the usual Black-Scholes formula by a feedforward neural network model. This functional shape is obtained when the option pricing function is homogeneous of degree one with respect to the underlying asset price (S-t) and the strike price (K). We show that pricing accuracy gains can be made by exploiting this generalized Black-Scholes shape. Instead of setting up a learning network mapping the ratio S-t/K and the time to maturity ( tau) directly into the derivative price, we break down the pricing function into two parts, one controlled by the ratio S-t/K, the other one by a function of time to maturity. The results indicate that the homogeneity hint always reduces the out-of-sample mean squared prediction error compared with a feedforward neural network with no hint. Both feedforward network models, with and without the hint, provide similar delta-hedging errors that are small relative to the hedging performance of the Black-Scholes model. However, the model with hint produces a more stable hedging performance. (C) 2000 Elsevier Science S.A. All rights reserved.