Abstract:

This article establishes that, in a one-dimensional diffusion world, any contingent claim's delta is bounded by its delta at maturity and, if its payoff is convex, its current value is convex in the underlying's value. A decline in the present value of the exercise price can be associated with a decline in a call's price. Bounds on call prices and deltas are derived for the case when the underlying's volatility is bounded. If the underlying follows a multi-dimensional diffusion (a stochastic volatility world), or a discontinuous or non-Markovian process, call prices can be decreasing, concave function of the underlying's value.

Website