Properties of option prices in models with jumps

Details Properties of option prices in models with jumps Properties of option prices in models with jumps

2005-09-10

arxiv.org/abs/math/0509232v2

Mathematics

Analysis of PDEs

14 pages

Scientific paper

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.

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