General Properties of Option Prices

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'...

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Bibliographic Details
Published in:The Journal of finance (New York) 1996-12, Vol.51 (5), p.1573-1610
Main Authors: BERGMAN, YAACOV Z., GRUNDY, BRUCE D., WIENER, ZVI
Format: Article
Language:English
Subjects:
Call options
Contingent claims
Determinism
Dividends
Economic models
Economic theory
Financial economics
Interest rates
Option pricing
Price volatility
Prices
Pricing policies
Put & call options
Rate setting
Securities prices
Stock options
Stock prices
Strike prices
Volatility
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Summary: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.
ISSN:0022-1082
1540-6261
DOI:10.1111/j.1540-6261.1996.tb05218.x