We propose a neural network approach to price EU call options that significantly outperforms some existing pricing models and comes with guarantees that its predictions are economically reasonable. To achieve this, we introduce a class of gated neural networks that automatically learn to divide-and-conquer the problem space for robust and accurate pricing. We then derive instantiations of these networks that are 'rational by design' in terms of naturally encoding a valid call option surface that enforces no arbitrage principles. This integration of human insight within data-driven learning provides significantly better generalisation in pricing performance due to the encoded inductive bias in the learning, guarantees sanity in the model's predictions, and provides econometrically useful byproduct such as risk neutral density.
There is a long history of computer scientists trying to solve option pricing using neural networks @cite_10 . Option pricing can be seen a standard regression task for which there are many established methods and neural networks (rebranded ) are one of the most popular choices.
@cite_10
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A neural network model that processes financial input data is developed to estimate the market price of options at closing. The network's ability to estimate closing prices is compared to the Black-Scholes model, the most widely used model for the pricing of options. Comparisons reveal that the mean squared error for the neural network is less than that of the Black-Scholes model in about half of the cases examined. The differences and similarities in the two modeling approaches are discussed. The neural network, which uses the same financial data as the Black-Scholes model, requires no distribution assumptions and learns the relationships between the financial input data and the option price from the historical data. The option-valuation equilibrium model of Black-Scholes determines option prices under the assumptions that prices follow a continuous time path and that the instantaneous volatility is nonstochastic. Abstract A feedforward neural network which can account for nonlinear relationships was used to compare ARIMA and neural network price forecasting performance. Data used was monthly live cattle and wheat prices from 1950 through 1990. The experiment was repeated seven times for successive three year periods. This involved using a walk forward or sliding window approach from 1970 through 1990 which generated out of sample results. The neural network models achieved a 27 percent and 56 percent lower mean squared error than ARIMA model. The absolute mean error and mean absolute percent error were also lower for the neural network models. The neural network models were able to capture a significant number of turning points for both wheat and cattle, while the ARIMA model was only able to do so for wheat. Since this forecasting method is not problem specific and uses only past prices, it can be applied to other forecasting problems such as stocks and other financial prices. In recent years, machine learning research has gained momentum: new developments in the field of deep learning allow for multiple levels of abstraction and are starting to supersede well-known and powerful tree-based techniques mainly operating on the original feature space. All these methods can be applied to various fields, including finance. This paper implements and analyzes the effectiveness of deep neural networks (DNN), gradient-boosted-trees (GBT), random forests (RAF), and several ensembles of these methods in the context of statistical arbitrage. Each model is trained on lagged returns of all stocks in the S&P 500, after elimination of survivor bias. From 1992 to 2015, daily one-day-ahead trading signals are generated based on the probability forecast of a stock to outperform the general market. The highest k probabilities are converted into long and the lowest k probabilities into short positions, thus censoring the less certain middle part of the ranking. Empirical findings are promising. A simple, equal-weighted ensemble (ENS1) consisting of one deep neural network, one gradient-boosted tree, and one random forest produces out-of-sample returns exceeding 0.45 percent per day for k=10, prior to transaction costs. Irrespective of the fact that profits are declining in recent years, our findings pose a severe challenge to the semi-strong form of market efficiency. Neural network predictor is widely applicable in intelligent forecast. However, it encounters the crucial problem that the predicted values always cannot achieve the satisfactory results because the generalization capability in neural network predictor can't perform extrapolation well. Therefore, this study introduced an integrated predictor to compare with neural network predictor utilized for the applications of non-periodic short-term time series forecast. This proposed predictor in fact is an integrated model, combing a grey prediction model and a cumulative least squared linear prediction model, with the technique of automatically compensating a possible overestimated predicted value by a potential damped predicted value around those predicting points having locally extreme high or low value. The verification of this study also experiments successfully in the stock price indexes forecast, and the results out of integrated predictor achieved the best accuracy on the predicted stock price indexes compared with Back-Propagation neural network predictor, Box-Jenkins, and Holt-Winters smoothing.