General Properties of Option Prices
研究了一维扩散过程及特定随机波动率下期权价格的性质，发现其Delta有界，且当收益函数凸（凹）时价格函数也凸（凹）；但在更一般条件下，看涨期权价格可能在某些区间内随标的资产价格递减、随时间递增、随利率递减。
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.