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Properties of option prices in models with jumps

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  • Erik Ekstrom
  • Johan Tysk

Abstract

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.

Suggested Citation

  • Erik Ekstrom & Johan Tysk, 2005. "Properties of option prices in models with jumps," Papers math/0509232, arXiv.org, revised Nov 2005.
  • Handle: RePEc:arx:papers:math/0509232
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    File URL: http://arxiv.org/pdf/math/0509232
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    References listed on IDEAS

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    1. Bergman, Yaacov Z & Grundy, Bruce D & Wiener, Zvi, 1996. " General Properties of Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1573-1610, December.
    2. N. Bellamy & M. Jeanblanc, 2000. "Incompleteness of markets driven by a mixed diffusion," Finance and Stochastics, Springer, vol. 4(2), pages 209-222.
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