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Filtration Reduction and Completeness in Jump-Diffusion Models

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  • Karen Grigorian
  • Robert Jarrow

Abstract

This paper studies the pricing and hedging of derivatives in frictionless and competitive, but incomplete jump-diffusion markets. A unique equivalent martingale measure (EMM) is obtained using filtration reduction to a fictitious complete market. This unique EMM in the fictitious market is uplifted to the original economy using the notion of consistency. For pedagogical purposes, we begin with simple setups and progressively extend to models of increasing generality.

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  • Karen Grigorian & Robert Jarrow, 2023. "Filtration Reduction and Completeness in Jump-Diffusion Models," Papers 2304.06202, arXiv.org, revised Jan 2024.
    • Handle: RePEc:arx:papers:2304.06202
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    References listed on IDEAS

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    1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    2. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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