Local volatility function approximation using reconstructed radial basis function networks

Abstract

Modelling volatility smile is very important in financial practice for pricing and hedging derivatives. In this paper, a novel learning method to approximate a local volatility function from a finite market data set is proposed. The proposed method trains a RBF network with fewer volatility data and finds an optimized network through option pricing error minimization. Numerical experiments are conducted on S&P 500 call option market data to illustrate a local volatility surface estimated by the method.