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Convexity preserving jump-diffusion models for option pricing

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  • Erik Ekstrom
  • Johan Tysk

Abstract

We investigate which jump-diffusion models are convexity preserving. The study of convexity preserving models is motivated by monotonicity results for such models in the volatility and in the jump parameters. We give a necessary condition for convexity to be preserved in several-dimensional jump-diffusion models. This necessary condition is then used to show that, within a large class of possible models, the only convexity preserving models are the ones with linear coefficients.

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  • Erik Ekstrom & Johan Tysk, 2006. "Convexity preserving jump-diffusion models for option pricing," Papers math/0601526, arXiv.org.
    • Handle: RePEc:arx:papers:math/0601526
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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. Masaaki Kijima, 2002. "Monotonicity And Convexity Of Option Prices Revisited," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 411-425, October.
    3. 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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    Cited by:

    1. Erik Ekstrom & Johan Tysk, 2007. "Convexity theory for the term structure equation," Papers math/0702435, arXiv.org.

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