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Properties Of Option Prices In Models With Jumps

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  • Erik Ekström
  • 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.

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  • Erik Ekström & Johan Tysk, 2007. "Properties Of Option Prices In Models With Jumps," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 381-397, July.
    • Handle: RePEc:bla:mathfi:v:17:y:2007:i:3:p:381-397
    DOI: 10.1111/j.1467-9965.2007.00308.x
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    Cited by:

    1. Jonas Al-Hadad & Zbigniew Palmowski, 2020. "Perpetual American options with asset-dependent discounting," Papers 2007.09419, arXiv.org, revised Jan 2021.
    2. José Fajardo & Ernesto Mordecki, 2006. "Skewness Premium with Lévy Processes," IBMEC RJ Economics Discussion Papers 2006-04, Economics Research Group, IBMEC Business School - Rio de Janeiro.

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