Premium
General Properties of Option Prices
Author(s) -
BERGMAN YAACOV Z.,
GRUNDY BRUCE D.,
WIENER ZVI
Publication year - 1996
Publication title -
the journal of finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 18.151
H-Index - 299
eISSN - 1540-6261
pISSN - 0022-1082
DOI - 10.1111/j.1540-6261.1996.tb05218.x
Subject(s) - infimum and supremum , stochastic game , volatility (finance) , concave function , mathematical economics , economics , econometrics , bounded function , regular polygon , mathematics , markov process , function (biology) , stochastic volatility , combinatorics , statistics , mathematical analysis , geometry , evolutionary biology , biology
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.