A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks

We 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.

Hypothesizing Device Mechanisms: Opening Up the Black Box

I describe an approach to forming hypotheses about hidden mechanism configurations within devices given external observations and a vocabulary of primitive mechanisms. An implemented causal modelling system called JACK constructs explanations for why a second piece of toast comes out lighter, why the slide in a tire gauge does not slip back inside when the gauge is removed from the tire, and how in a refrigerator a single substance can serve as a heat sink for the interior and a heat source for the exterior. I report the number of hypotheses admitted for each device example, and provide empirical results which isolate the pruning power due to different constraint sources.