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On the range of options prices (*)

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  • 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)

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    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.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 1 (1997)
    Issue (Month): 2 ()
    Pages: 131-140

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    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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    Related research

    Keywords: Contingent claim valuation; incomplete model; purely discontinuous process; martingale measures;

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