IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

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

  • Garcia, Rene
  • Gencay, Ramazan

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 forme fondée sur l'homogéné

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

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Econometrics.

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

in new window

Handle: RePEc:eee:econom:v:94:y:2000:i:1-2:p:93-115
Contact details of provider: Web page:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. James M. Hutchinson & Andrew W. Lo & Tomaso Poggio, 1994. "A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks," NBER Working Papers 4718, National Bureau of Economic Research, Inc.
  2. 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.
  3. 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.
  4. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, 04.
  5. René Garcia & Eric Renault, 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," Working Papers 98-10, Centre de Recherche en Economie et Statistique.
  6. 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.
  7. 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.
  8. Jondeau, Eric & Rockinger, Michael, 1998. "Reading the Smile: The Message Conveyed by Methods which Infer Risk Neutral Densities," CEPR Discussion Papers 2009, C.E.P.R. Discussion Papers.
  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. repec:taf:emetrv:v:13:y:1994:i:1:p:1-91 is not listed on IDEAS
  11. Gouriéroux, Christian & Monfort, Alain & Tenreiro, Carlos, 1994. "Kernel m-estimators : non parametric diagnostics for structural models," CEPREMAP Working Papers (Couverture Orange) 9405, CEPREMAP.
  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. 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.
  15. 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).
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:94:y:2000:i:1-2:p:93-115. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.