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On the range of options prices (*)

Author

Listed:
  • Ernst Eberlein

    (Institut fØr Mathematische Stochastik, UniversitÄt Freiburg, Eckerstrasse 1, D-79104 Freiburg, Germany)

  • Jean Jacod

    (Laboratoire de ProbabilitÊs , UniversitÊ Pierre et Marie Curie, Tour 56, 4 Place Jussieu, F-75 252 Paris Cedex, France)

Abstract

In this paper we consider the valuation of an option with time to expiration $T$ and pay-off function $g$ which is a convex function (as is a European call option), and constant interest rate $r$, in the case where the underlying model for stock prices $(S_t)$ is a purely discontinuous process (hence typically the model is incomplete). The main result is that, for "most" such models, the range of the values of the option, using all possible equivalent martingale measures for the valuation, is the interval $(e^{-rT}g(e^{rT}S_0),S_0)$, this interval being the biggest interval in which the values must lie, whatever model is used.

Suggested Citation

  • Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
    • Handle: RePEc:spr:finsto:v:1:y:1997:i:2:p:131-140
    Note: received: November 1995; final version received: November 1996
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    More about this item

    Keywords

    Contingent claim valuation; incomplete model; purely discontinuous process; martingale measures;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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