General Properties of Option Prices

Yaacov Z Bergman, Bruce D Grundy and Zvi Wiener

Journal of Finance, 1996, vol. 51, issue 5, 1573-1610

Abstract: When the underlying price process is a one-dimensional diffusion, as well as in certain restricted stochastic volatility settings, a contingent claim's delta is bounded by the infimum and supremum of its delta at maturity. Further, if the claim's payoff is convex (concave), the claim's price is a convex (concave) function of the underlying asset's value. However, when volatility is less specialized, or when the underlying process is discontinuous or non-Markovian, a call's price can be a decreasing, concave function of the underlying price over some range, increasing with the passage of time, and decreasing in the level of interest rates. Copyright 1996 by American Finance Association.

Date: 1996
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