On the Range of Options Prices

FINANCE AND STOCHASTICS, Vol. I No. 2, 1997

Posted: 10 Apr 1997

See all articles by Ernst Eberlein

Ernst Eberlein

University of Freiburg

Jean Jacod

Université Paris VI Pierre et Marie Curie

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 (exp{rT}g(exp{rT}S_0),S_0), this interval being the biggest interval in which the values must lie, whatever model is used.

JEL Classification: G13

Suggested Citation

Eberlein, Ernst and Jacod, Jean, On the Range of Options Prices. FINANCE AND STOCHASTICS, Vol. I No. 2, 1997. Available at SSRN: https://ssrn.com/abstract=8270

Ernst Eberlein (Contact Author)

University of Freiburg ( email )

Department of Mathematical Stochastics
Eckerstrasse 1
D-79104, Freiburg
Germany
++49 761 203 5660 (Phone)
++49 761 203 5661 (Fax)

Jean Jacod

Université Paris VI Pierre et Marie Curie ( email )

4, Place Jussieu, B.P. 169
Laboratoire de Probabilites
F-75252-Paris Cedex 05
France
01 44 27 53 21 (Phone)

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