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MONOTONICITY AND CONVEXITY OF OPTION PRICES REVISITED
Author(s) -
Kijima Masaaki
Publication year - 2002
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2002.tb00131.x
Subject(s) - convexity , monotonic function , economics , mathematical economics , regular polygon , econometrics , stock price , stochastic game , volatility (finance) , concave function , volatility smile , implied volatility , mathematics , financial economics , mathematical analysis , paleontology , geometry , series (stratigraphy) , biology
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.