## A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks, Issue 4718We propose a nonparametric method for estimating derivative financial asset pricing formulae using learning networks. To demonstrate feasibility, we first simulate Black-Scholes option prices and show that learning networks can recover the Black-Scholes formula from a two-year training set of daily options prices, and that the resulting network formula can be used successfully to both price and delta-hedge options out-of-sample. For comparison, we estimate models using four popular methods: ordinary least squares, radial basis functions, multilayer perceptrons, and projection pursuit. To illustrate practical relevance, we also apply our approach to S & P 500 futures options data from 1987 to 1991. Option pricing, Learning, Finance, Black-Scholes, Hedging. |

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500 futures options 500 independent test 500 test sets absolute delta-hedging error absolute tracking error approximation error asset Black-Scholes delta-hedging error Black-Scholes formula Black-Scholes model call options CBOE data points delta-hedging strategy estimated across 500 Estimated prediction errors Fraction of 500 futures contracts geometric Brownian motion HEDGING DERIVATIVE SECURITIES independent test paths learning networks linear models Linear-1 Linear-2 RBF Linear-2 RBF PPR MLP networks multilayer perceptron network pricing formula non-dividend-paying stock currently nonparametric NONPARAMETRIC APPROACH number of data number of parameters option prices option pricing formula options with strike p-value particular performance measures Poggio and Girosi PPR MLP B-S PPR networks priced at $50 pricing and hedging projection pursuit regression Radial Basis Functions RBF networks RBF PPR MLP replicating portfolio S&P 500 futures sample paths Section simulated training path smoothness specification statistical stock currently priced strike price subperiods techniques term Linear-1 Linear-2 time-to-maturity T—t months Tomaso Poggio total number