General Properties of Option Prices

General Properties of Option Prices 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 always bounded by the in mum and supremum of its delta at maturity. Further, if the claim's payoff is convex (concave), then 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 price follows a discontinuous or non-Markovian process, then call prices can have properties very different from those of the Black-Scholes model: 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. Much of th

General Properties of Option Prices.

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.