This study examines the option pricing method which employs Artificial Neural Networks and Wiener-Itô Chaos asymptotic expansion. In particular, the machine learning model is trained on the difference between the exact option price and its approximation, obtained through the Wiener-Itô Chaos expansion of the underlying. This examination compares this method with the one that applies the Artificial Neural Networks directly on the exact price. Unlike previous research, this study quantifies their prediction accuracy with root mean squared error and mean absolute error measures. In addition to previously examined derivatives, this option pricing procedure is applied to two new ones, i.e. two Down-and-In single barrier options: the first under the Costant Elasticity of Variance and the second under a non linear volatility model. Moreover, the two methods are compared in their best performing scenario, i.e. when the hyper-parameters of the Artificial Neural Networks are tuned. In every case examined, the method that trains on the specified residual term offers more accurate and stable predictions than the one whose Artificial Neural Network trains directly on the option price.
Questo studio esamina un metodo di valutazione di opzioni finanziarie che si serve di reti neurali e dello sviluppo in caos di Wiener-Itô. In particolare, il modello di machine learning utilizza la differenza tra il prezzo esatto del derivato e la sua approssimazione, ottenuta attraverso lo sviluppo asintotico in caos di Wiener Itô del sottostante. Questa valutazione mette a confronto questo metodo con quello che applica la rete neurale direttamente al prezzo esatto. Rispetto a studi precedenti, questa trattazione quantifica l’accuratezza delle previsioni attraverso la radice dell’errore quadratico medio e l’errore assoluto medio. Oltre ai derivati già esaminati in precedenza, questa procedura di prezzatura è applicata a due nuovi casi, ovvero due opzioni barriera Down-and-In, il cui sottostante evolve secondo due modelli: uno, a elasticità di variazione costante, l’altro, a volatilità non lineare. Inoltre, i due metodi sono confrontati nel loro scenario migliore, ossia quando gli iperparametri della rete neurale sono ottimizzati. In ogni caso esaminato, il metodo che si serve della differenza tra prezzo esatto e approssimazione offre previsioni più accurate e stabili rispetto a quello la cui rete neurale è applicata direttamente al prezzo esatto.
Option pricing with Artificial Neural Networks and Wiener-Itô Chaos expansion approximation formulae
Buccioni, Valentina
2021/2022
Abstract
This study examines the option pricing method which employs Artificial Neural Networks and Wiener-Itô Chaos asymptotic expansion. In particular, the machine learning model is trained on the difference between the exact option price and its approximation, obtained through the Wiener-Itô Chaos expansion of the underlying. This examination compares this method with the one that applies the Artificial Neural Networks directly on the exact price. Unlike previous research, this study quantifies their prediction accuracy with root mean squared error and mean absolute error measures. In addition to previously examined derivatives, this option pricing procedure is applied to two new ones, i.e. two Down-and-In single barrier options: the first under the Costant Elasticity of Variance and the second under a non linear volatility model. Moreover, the two methods are compared in their best performing scenario, i.e. when the hyper-parameters of the Artificial Neural Networks are tuned. In every case examined, the method that trains on the specified residual term offers more accurate and stable predictions than the one whose Artificial Neural Network trains directly on the option price.File | Dimensione | Formato | |
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Descrizione: Option pricing with Artificial Neural Networks and Wiener-Itô Chaos expansion approximation formulae - Valentina Buccioni - Master's Thesis
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https://hdl.handle.net/10589/202861