General Properties of Option Prices

  • Author(s): YAACOV Z. BERGMAN, BRUCE D. GRUNDY, ZVI WIENER
  • Published: Apr 30, 2012
  • Pages: 1573-1610
  • DOI: 10.1111/j.1540-6261.1996.tb05218.x

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.

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