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<p>In a standard no-arbitrage continuous-time model, this paper characterizes a digital asset’s price process as being decomposed into four components: its fundamental value and three different types of bubbles, labeled type 1, 2 and 3. Type 1 bubbles are permanent, type 2 are long-horizon, and type 3 are short-horizon. Only type 3 (short-horizon) bubbles are not martingales under an equivalent local martingale measure. This decomposition implies the standard derivative pricing methodology does not apply to digital assets whose market prices reflect type 3 (short-horizon) bubbles. Modifications to the existing derivative pricing theory needed for digital assets with price bubbles are explored herein.</p>

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Digital assets, bubbles, and derivative prices

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Robert A. Jarrow

摘要

In a standard no-arbitrage continuous-time model, this paper characterizes a digital asset’s price process as being decomposed into four components: its fundamental value and three different types of bubbles, labeled type 1, 2 and 3. Type 1 bubbles are permanent, type 2 are long-horizon, and type 3 are short-horizon. Only type 3 (short-horizon) bubbles are not martingales under an equivalent local martingale measure. This decomposition implies the standard derivative pricing methodology does not apply to digital assets whose market prices reflect type 3 (short-horizon) bubbles. Modifications to the existing derivative pricing theory needed for digital assets with price bubbles are explored herein.