3,706 research outputs found
A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks
We propose a nonparametric method for estimating the pricing formula of a derivative asset using learning networks. Although not a substitute for the more traditional arbitrage-based pricing formulas, network pricing formulas may be more accurate and computationally more efficient alternatives when the underlying asset's price dynamics are unknown, or when the pricing equation associated with no-arbitrage condition cannot be solved analytically. To assess the potential value of network pricing formulas, we 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 function networks, multilayer perceptron networks, and projection pursuit. To illustrate the practical relevance of our network pricing approach, we apply it to the pricing and delta-hedging of S&P 500 futures options from 1987 to 1991.
Image denoising with multi-layer perceptrons, part 1: comparison with existing algorithms and with bounds
Image denoising can be described as the problem of mapping from a noisy image
to a noise-free image. The best currently available denoising methods
approximate this mapping with cleverly engineered algorithms. In this work we
attempt to learn this mapping directly with plain multi layer perceptrons (MLP)
applied to image patches. We will show that by training on large image
databases we are able to outperform the current state-of-the-art image
denoising methods. In addition, our method achieves results that are superior
to one type of theoretical bound and goes a large way toward closing the gap
with a second type of theoretical bound. Our approach is easily adapted to less
extensively studied types of noise, such as mixed Poisson-Gaussian noise, JPEG
artifacts, salt-and-pepper noise and noise resembling stripes, for which we
achieve excellent results as well. We will show that combining a block-matching
procedure with MLPs can further improve the results on certain images. In a
second paper, we detail the training trade-offs and the inner mechanisms of our
MLPs
Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review
The paper characterizes classes of functions for which deep learning can be
exponentially better than shallow learning. Deep convolutional networks are a
special case of these conditions, though weight sharing is not the main reason
for their exponential advantage
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