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Pricing and hedging derivative securities with neural networks and a homogeneity hint

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  • Garcia, Rene
  • Gencay, Ramazan

Abstract

We 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 ¸ l'aide d'un modèle de réseaux de neurones, nous estimons une formule d'évaluation d'option généralisée qui a une forme fonctionnelle similaire à la formule de Black-Scholes habituelle. Cette forme fonctionnelle s'obtient lorsque le prix d'option est une fonction homogène de degré un par rapport au prix de l'actif sous-jacent et au prix d'exercice. Nous montrons que cette forme généralisée de Black-Scholes nous permet de prévoir plus précisément les prix d'options. Au lieu de construire notre réseau d'apprentissage en entrant directement le rapport prix de l'actif sous-jacent / prix d'exercice et l'échéance dans la fonction de prix, nous décomposons cette dernière en deux parties, l'une contrôlée par le rapport prix de l'actif sous-jacent / prix d'exercice l'autre par une fonction de l'échéance. Les résultats indiquent que la f

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 94 (2000)
Issue (Month): 1-2 ()
Pages: 93-115

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Handle: RePEc:eee:econom:v:94:y:2000:i:1-2:p:93-115

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Web page: http://www.elsevier.com/locate/jeconom

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  1. Yacine Aït-Sahalia & Andrew W. Lo, . "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," CRSP working papers 332, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
  2. Hutchinson, James M & Lo, Andrew W & Poggio, Tomaso, 1994. " A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks," Journal of Finance, American Finance Association, vol. 49(3), pages 851-89, July.
  3. repec:taf:emetrv:v:13:y:1994:i:1:p:1-91 is not listed on IDEAS
  4. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "Nonparametric estimation of American options' exercise boundaries and call prices," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1829-1857, October.
  5. Jondeau, Eric & Rockinger, Michael, 2000. "Reading the smile: the message conveyed by methods which infer risk neutral densities," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 885-915, December.
  6. Swanson, Norman R & White, Halbert, 1995. "A Model-Selection Approach to Assessing the Information in the Term Structure Using Linear Models and Artificial Neural Networks," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 265-75, July.
  7. René Garcia & Eric Renault, 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," Working Papers 98-10, Centre de Recherche en Economie et Statistique.
  8. GHYSELS, Eric & PATILEA, Valentin & RENAULT, Eric & TORRES, Olivier, 1997. "Nonparametric methods and option pricing," CORE Discussion Papers 1997075, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237.
  10. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  11. Mark Broadie & Jérôme B. Detemple & Eric Ghysels & Olivier Torrès, 1996. "American Options with Stochastic Dividends and Volatility: A Nonparametric Investigation," CIRANO Working Papers 96s-26, CIRANO.
  12. Bailey, Warren & Stulz, René M., 1989. "The Pricing of Stock Index Options in a General Equilibrium Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(01), pages 1-12, March.
  13. Turnbull, Stuart M & Milne, Frank, 1991. "A Simple Approach to Interest-Rate Option Pricing," Review of Financial Studies, Society for Financial Studies, vol. 4(1), pages 87-120.
  14. Gouriéroux, Christian & Monfort, Alain & Tenreiro, Carlos, 1994. "Kernel m-estimators : non parametric diagnostics for structural models," CEPREMAP Working Papers (Couverture Orange) 9405, CEPREMAP.
  15. repec:fth:louvco:9775 is not listed on IDEAS
  16. Amin, Kaushik I & Ng, Victor K, 1993. " Option Valuation with Systematic Stochastic Volatility," Journal of Finance, American Finance Association, vol. 48(3), pages 881-910, July.
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