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A P.D.E. approach to Asian options: analytical and numerical evidence

Author

Listed:
  • Bénédicte Alziary

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, IMT - Institut de Mathématiques de Toulouse UMR5219 - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - UT2J - Université Toulouse - Jean Jaurès - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Paul Décamps

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, TSM - Toulouse School of Management Research - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - CNRS - Centre National de la Recherche Scientifique - TSM - Toulouse School of Management - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse)

  • Pierre-François Koehl

    (ENSAE-CREST, Institut Polytechnique de Paris)

Abstract

We first derive a one-state-variable partial differential equation, easy to implement, which characterizes the price of a European type Asian option. This result is explained and related to previous literature. We then derive new results on the hedging of an Asian option and propose analytical and numerical analysis on the comparison between Asian and European options. Our methodology which applies to "fixed-strike" Asian options as well as to "floating-strike" Asian options completes and clarifies various results in the literature. In this paper we focus on "backward-starting" Asian options. Our approach is quite general however, and we explain how to adapt our main results to the case of "forward-starting" Asian options.

Suggested Citation

  • Bénédicte Alziary & Jean-Paul Décamps & Pierre-François Koehl, 1997. "A P.D.E. approach to Asian options: analytical and numerical evidence," Post-Print hal-05485005, HAL.
    • Handle: RePEc:hal:journl:hal-05485005
    DOI: 10.1016/S0378-4266(96)00057-X
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