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Learning Short-Option Valuation In The Presence Of Rare Events

Author

Listed:
  • M. RABERTO

    (DIBE, Università di Genova, via Opera Pia 11a, I-16145 Genova, Italy)

  • G. CUNIBERTI

    (Max-Planck-Institut PKS, Nöthnitzer Str. 38, D-01187, Dresden, Germany)

  • M. RIANI

    (INFM and Dipartimento di Fisica, Università di Genova, via Dodecaneso 33, I-16146 Genova, Italy)

  • E. SCALES

    (Lab33 S.r.l., corso Perrone 24, 1-16152 Genova, Italy)

  • F. MAINARDI

    (INFN and Dipartimento di Fisica, Universitàdi Bologna, via Irnerio 46, I-40126 Bologna, Italy)

  • G. SERVIZI

    (INFN and Dipartimento di Fisica, Universitàdi Bologna, via Irnerio 46, I-40126 Bologna, Italy)

Abstract

We extend the neural-network approach for the valution of financial derivatives developed by Hutchinsonet al.[1] to the case of fat-tailed distributions of the underlying asset returns. We use a two-layer perceptron with three inputs, four hidden neurons, and one output. The input parameters of the network are: the simulated price of the underlying assetFdivided by the strike priceE, the time-to-maturityT, and the ratio|F-E|/T. The latter takes into account the volatility smile, whereas the priceFis generated by the method of Gorenfloet al.[2] based on fractional calculus. The output parameter is the call priceCoverE. The learning-set option priceCis computed by means of a formula given by Bouchaud and Potters [3, 4]. Option prices obtained by means of this learning scheme are compared with LIFFE option prices on German treasury bond (BUND) futures.

Suggested Citation

  • M. Raberto & G. Cuniberti & M. Riani & E. Scales & F. Mainardi & G. Servizi, 2000. "Learning Short-Option Valuation In The Presence Of Rare Events," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 563-564.
  • Handle: RePEc:wsi:ijtafx:v:03:y:2000:i:03:n:s0219024900000590
    DOI: 10.1142/S0219024900000590
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