Pricing and hedging derivative securities with neural networks and a homogeneity hint
AbstractWe estimate a generalized option pricing formula that has a functional shape similar to the usual Black-Scholes formula by a feedforward neural network model. This functional shape is obtained when the option pricing function is homogeneous of degree one with respect to the underlying asset price and the strike price. We show that pricing accuracy gains can be made by exploiting this generalized Black-Scholes shape. Instead of setting up a learning network mapping the ratio asset price/strike price and the time to maturity directly into the derivative price, we break down the pricing function into two parts, one controlled by the ratio asset price/strike price, the other one by a function of time to maturity. The results indicate that the homogeneity hint always reduces the out-of-sample mean squared prediction error compared with a feedforward neural network with no hint. Both feedforward network models, with and without the hint, provide similar delta-hedging errors that are small relative to the hedging performance of the Black-Scholes model. However, the model with hint produces a more stable hedging performance Â¸ l'aide d'un modÃ¨le de rÃ©seaux de neurones, nous estimons une formule d'Ã©valuation d'option gÃ©nÃ©ralisÃ©e qui a une forme fonctionnelle similaire Ã la formule de Black-Scholes habituelle. Cette forme fonctionnelle s'obtient lorsque le prix d'option est une fonction homogÃ¨ne de degrÃ© un par rapport au prix de l'actif sous-jacent et au prix d'exercice. Nous montrons que cette forme gÃ©nÃ©ralisÃ©e de Black-Scholes nous permet de prÃ©voir plus prÃ©cisÃ©ment les prix d'options. Au lieu de construire notre rÃ©seau d'apprentissage en entrant directement le rapport prix de l'actif sous-jacent / prix d'exercice et l'Ã©chÃ©ance dans la fonction de prix, nous dÃ©composons cette derniÃ¨re en deux parties, l'une contrÃ´lÃ©e par le rapport prix de l'actif sous-jacent / prix d'exercice l'autre par une fonction de l'Ã©chÃ©ance. Les rÃ©sultats indiquent que la f
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 94 (2000)
Issue (Month): 1-2 ()
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Web page: http://www.elsevier.com/locate/jeconom
Other versions of this item:
- René Garcia & Ramazan Gençay, 1998. "Pricing and Hedging Derivative Securities with Neural Networks and a Homogeneity Hint," CIRANO Working Papers 98s-35, CIRANO.
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