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Pricing and Hedging Derivative Securities with Neural Networks and a Homogeneity Hint *
| Content Provider | Semantic Scholar |
|---|---|
| Author | Garcia, René Gencay, Ramazan |
| Copyright Year | 1998 |
| 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 (S t ) and the strike price (K). 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 S t /K and the time to maturity (q) directly into the derivative price, we break down the pricing function into two parts, one controlled by the ratio S t /K, 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. This paper has bene"ted from the comments of seminar participants at Cornell University, CREST, Ohio State University, McGill University, UniversiteH du QueH bec à MontreH al, and the 1998 Econometric Society Summer Meeting (MontreH al). We thank Sami Bengio, Yoshua Bengio, JeanPaul Laurent, Nour Meddahi, and Eric Renault for useul discussions and comments. ReneH Garcia gratefully acknowledges "nancial support from the Social Sciences and Humanities Research Council of Canada, the Fonds de la Formation de Chercheurs et l'Aide à la Recherche du QueH bec (FCAR) and the Natural Sciences and Engineering Council of Canada. Ramazan Genc7 ay thanks the Social Sciences and Humanities Research Council of Canada and the Natural Sciences and Engineering Research Council of Canada for "nancial support. *Corresponding author. Tel.: #1-514-343-3930; fax: #1-514-343-5831. 0304-4076/00/$ see front matter ( 2000 Elsevier Science S.A. All rights reserved. PII: S 0 3 0 4 4 0 7 6 ( 9 9 ) 0 0 0 1 8 4 However, the model with hint produces a more stable hedging performance. ( 2000 Elsevier Science S.A. All rights reserved. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://finance.martinsewell.com/option-pricing/GaGe98.pdf |
| Alternate Webpage(s) | http://www.cirano.qc.ca/pdf/publication/98s-35.pdf |
| Alternate Webpage(s) | http://www.cirano.qc.ca/files/publications/98s-35.pdf |
| Alternate Webpage(s) | http://yoksis.bilkent.edu.tr/pdf/files/10.1016-S0304-4076(99)00018-4.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
