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PROPERTIES OF OPTION PRICES IN MODELS WITH JUMPS
Author(s) -
Ekström Erik,
Tysk Johan
Publication year - 2007
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.1467-9965.2007.00308.x
Subject(s) - convexity , monotonic function , martingale (probability theory) , mathematics , jump , mathematical economics , econometrics , regular polygon , volatility (finance) , valuation of options , economics , stochastic volatility , bellman equation , mathematical analysis , financial economics , physics , geometry , quantum mechanics
We study convexity and monotonicity properties of option prices in a model with jumps using the fact that these prices satisfy certain parabolic integro–differential equations. Conditions are provided under which preservation of convexity holds, i.e., under which the value, calculated under a chosen martingale measure, of an option with a convex contract function is convex as a function of the underlying stock price. The preservation of convexity is then used to derive monotonicity properties of the option value with respect to the different parameters of the model, such as the volatility, the jump size, and the jump intensity.