European Options in Continuous Time

  • Robert J. Elliott
  • P. Ekkehard Kopp
Part of the Springer Finance book series (FINANCE)


In this chapter we develop a continuous time theory which is the analogue of that in Chapters 1 to 3. The simple model consists of a riskless bond and a risky asset, which can be thought of as a stock. The dynamics of our model are described in Section 7.1. The following two sections present the fundamental results of Girsanov and martingale representation. These are then applied to discuss the hedging and pricing of European options. In particular, we establish the famous results of Black and Scholes, results which are applied widely in the industry in spite of the simplified nature of the model.


Option Price Risky Asset Contingent Claim Standard Brownian Motion Martingale Measure 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Robert J. Elliott
    • 1
  • P. Ekkehard Kopp
    • 2
  1. 1.Department of Mathematical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Pro-Vice-Chancellors’ OfficeThe University of HullHullUK

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