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Semigroup theory applied to options

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  • D. I. Cruz-Báez
  • J. M. González-Rodríguez

Abstract

Black and Scholes (1973) proved that under certain assumptions about the market place, the value of a European option, as a function of the current value of the underlying asset and time, verifies a Cauchy problem. We give new conditions for the existence and uniqueness of the value of a European option by using semigroup theory. For this, we choose a suitable space that verifies some conditions, what allows us that the operator that appears in the Cauchy problem is the infinitesimal generator of a C 0 -semigroup T ( t ) . Then we are able to guarantee the existence and uniqueness of the value of a European option and we also achieve an explicit expression of that value.

Suggested Citation

  • D. I. Cruz-Báez & J. M. González-Rodríguez, 2002. "Semigroup theory applied to options," Journal of Applied Mathematics, Hindawi, vol. 2, pages 1-9, January.
    • Handle: RePEc:hin:jnljam:245081
    DOI: 10.1155/S1110757X02111041
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