scholarly journals Financial Option Valuation by Unsupervised Learning with Artificial Neural Networks

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 46
Author(s):  
Beatriz Salvador ◽  
Cornelis W. Oosterlee ◽  
Remco van der Meer
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Unsupervised Learning ◽  
Short Note ◽  
Classical Problem ◽  
Problem Formulation ◽  
Financial Options ◽  
Black Scholes ◽  
Option Values ◽  
Artificial Neural

Artificial neural networks (ANNs) have recently also been applied to solve partial differential equations (PDEs). The classical problem of pricing European and American financial options, based on the corresponding PDE formulations, is studied here. Instead of using numerical techniques based on finite element or difference methods, we address the problem using ANNs in the context of unsupervised learning. As a result, the ANN learns the option values for all possible underlying stock values at future time points, based on the minimization of a suitable loss function. For the European option, we solve the linear Black–Scholes equation, whereas for the American option we solve the linear complementarity problem formulation. Two-asset exotic option values are also computed, since ANNs enable the accurate valuation of high-dimensional options. The resulting errors of the ANN approach are assessed by comparing to the analytic option values or to numerical reference solutions (for American options, computed by finite elements). In the short note, previously published, a brief introduction to this work was given, where some ideas to price vanilla options by ANNs were presented, and only European options were addressed. In the current work, the methodology is introduced in much more detail.

scholarly journals European and American Options Valuation by Unsupervised Learning with Artificial Neural Networks

Proceedings ◽  
2020 ◽  
Vol 54 (1) ◽  
pp. 14
Author(s):  
Beatriz Salvador ◽  
Cornelis W. Oosterlee ◽  
Remco van der Meer
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Unsupervised Learning ◽  
Classical Problem ◽  
Problem Formulation ◽  
Financial Options ◽  
Black Scholes ◽  
Option Values ◽  
Artificial Neural ◽  
Stock Values

Artificial neural networks (ANNs) have recently also been applied to solve partial differential equations (PDEs). In this work, the classical problem of pricing European and American financial options, based on the corresponding PDE formulations, is studied. Instead of using numerical techniques based on finite element or difference methods, we address the problem using ANNs in the context of unsupervised learning. As a result, the ANN learns the option values for all possible underlying stock values at future time points, based on the minimization of a suitable loss function. For the European option, we solve the linear Black–Scholes equation, whereas for the American option, we solve the linear complementarity problem formulation.

Unsupervised Learning in Artificial Neural Networks

2008 ◽  
pp. 48-90
Author(s):  
Darryl Charles ◽  
Colin Fyfe ◽  
Daniel Livingstone ◽  
Stephen McGlinchey
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Unsupervised Learning ◽  
Input Data ◽  
Descent Methods ◽  
Training Set ◽  
Human Capabilities ◽  
Artificial Neural ◽  
Do So

With the artificial neural networks which we have met so far, we must have a training set on which we already have the answers to the questions which we are going to pose to the network. Yet humans appear to be able to learn (indeed some would say can only learn) without explicit supervision. The aim of unsupervised learning is to mimic this aspect of human capabilities and hence this type of learning tends to use more biologically plausible methods than those using the error descent methods of the last two chapters. The network must self-organise and to do so, it must react to some aspect of the input data - typically either redundancy in the input data or clusters in the data; i.e. there must be some structure in the data to which it can respond.

Beyond Black–Scholes: A Neural Networks-Based Approach to Options Pricing

2003 ◽  
Vol 06 (05) ◽  
pp. 469-489 ◽  
Author(s):  
Christopher A. Zapart
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Bootstrap Method ◽  
Feature Space ◽  
Options Pricing ◽  
Black Scholes Model ◽  
Volatility Model ◽  
Starting Point ◽  
Black Scholes ◽  
Artificial Neural

The paper presents two alternative schemes for pricing European and American call options, both based on artificial neural networks. The first method uses binomial trees linked to an innovative stochastic volatility model. The volatility model is based on wavelets and artificial neural networks. Wavelets provide a convenient signal/noise decomposition of the volatility in the non-linear feature space. Neural networks are used to infer future volatility levels from the wavelets feature space in an iterative manner. The bootstrap method provides the 95% confidence intervals for the options prices. In the second approach neural networks are trained with genetic algorithms in order to reverse-engineer the Black–Scholes formulae. The standard Black–Scholes model provides a starting point for an evolutionary training process, which yields improved options prices. Market options prices as quoted on the Chicago Board Options Exchange are used for performance comparison between the Black–Scholes model and the proposed options pricing schemes. The proposed models produce as good as and often better options prices than the conventional Black–Scholes formulae.

scholarly journals Formulation Of A Rational Option Pricing Model using Artificial Neural Networks

2020 ◽  
Author(s):  
Kaustubh yadav ◽  
Anubhuti yadav
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Option Pricing ◽  
Numerical Solutions ◽  
Options Pricing ◽  
Volatility Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Efficient Alternative ◽  
Artificial Neural

This paper inquires on the options pricing modeling using Artificial Neural Networks to price Apple(AAPL) European Call Options. Our model is based on the premise that Artificial Neural Networks can be used as functional approximators and can be used as an alternative to the numerical methods to some extent, for a faster and an efficient solution. This paper provides a neural network solution for two financial models, the BlackScholes-Merton model, and the calibrated-Heston Stochastic Volatility Model, we evaluate our predictions using the existing numerical solutions for the same, the analytic solution for the Black-Scholes equation, COS-Model for Heston’s Stochastic Volatility Model and Standard Heston-Quasi analytic formula. The aim of this study is to find a viable time-efficient alternative to existing quantitative models for option pricing.

scholarly journals Comparison study of CFD and artificial neural networks in predicting temperature fields induced by natural convention in a square enclosure

2019 ◽  
Vol 23 (6 Part A) ◽  
pp. 3481-3492
Author(s):  
Shiyu Zhou ◽  
Xiaoping Liu ◽  
Guangyue Du ◽  
Chuanze Liu ◽  
Yucheng Zhou
Keyword(s):  
Heat Transfer ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Natural Convection ◽  
Classical Problem ◽  
Temperature Fields ◽  
Ann Model ◽  
Artificial Neural ◽  
Relative Errors ◽  
Mean Square Errors

Natural convection in an enclosure is a classical problem in heat transfer field. In this study, natural convection induced by the heat source in the enclosure is studied with two analysis methods, i. e. CFD and artificial neural networks (ANN). The heat transfer in the enclosure is an unsteady process. During this process, the temperature fields in the enclosure are changing with time. The vertical temperature field of y = 0 at one moment is picked up for investigation. Firstly, FLUENT software which is a simulation program of CFD is adopted to simulate the temperature fields under different computation conditions. Then part of the simulation condition?s temperature data is picked for training an ANN model and the rest of data is used for validating the ANN model. It has been found from the comparison between the CFD simulation and ANN prediction that the two results have a good agreement with each other. In the comparison, the max relative errors are around 12%, mean relative errors are around 0.3%, mean square errors are around 0.6%, values of absolute fraction of variance are all not less than 0.99. The results demonstrated that the ANN prediction have enough accuracy.

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