MONOTONICITY AND CONVEXITY OF OPTION PRICES REVISITED

Masaaki Kijima

Mathematical Finance, 2002, vol. 12, issue 4, 411-425

Abstract: The Black‐Scholes option price is increasing and convex with respect to the initial stock price. increasing with respect to volatility and instantaneous interest rate, and decreasing and convex with respect to the strike price. These results have been extended in various directions. In particular, when the underlying stock price follows a one‐dimensional diffusion and interest rates are deterministic, it is well known that a European contingent claim's price written on the stock with a convex (concave. respectively) payoff function is also convex (concave) with respect to the initial stock price. This paper discusses extensions of such results under more general settings by simple arguments.

Date: 2002
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