Financial Option Valuation by Unsupervised Learning with Artificial Neural Networks
| Autor: | Cornelis W. Oosterlee, Remco van der Meer, Beatriz Salvador |
|---|---|
| Přispěvatelé: | Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Artificial neural network
Mathematical optimization Computer science General Mathematics Computational Finance (q-fin.CP) 010103 numerical & computational mathematics Black–Scholes model 01 natural sciences Multi-asset options FOS: Economics and business Quantitative Finance - Computational Finance 0502 economics and business Computer Science (miscellaneous) 0101 mathematics (non)linear PDEs Engineering (miscellaneous) multi-asset options Valuation (finance) 050208 finance Partial differential equation lcsh:Mathematics 05 social sciences Exotic option lcsh:QA1-939 Linear complementarity problem Loss function loss function Valuation of options Unsupervised learning artificial neural network |
| Zdroj: | Mathematics, Vol 9, Iss 46, p 46 (2021) RUC: Repositorio da Universidade da Coruña Universidade da Coruña (UDC) Mathematics, 9(1) RUC. Repositorio da Universidade da Coruña Universitat Oberta de Catalunya (UOC) Mathematics Volume 9 Issue 1 |
| ISSN: | 2227-7390 |
| Popis: | 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&ndash 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. |
| Databáze: | OpenAIRE |
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