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Martingale defects in the volatility surface and bubble conditions in the underlying

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  • Stahl, Philip
  • Blauth, Jérôme

Abstract

The martingale theory of bubbles enables testing for asset price bubbles by analyzing option prices. As recently shown by Piiroinen et al. (Asset price bubbles: an option-based indicator, 2018), the SABR model is a strict local martingale when its parameterization implies a positive correlation between stock and option prices. We operationalize this theoretical result and analyze stock price bubbles in 2576 stocks over 26 years. Martingale defect conditions are absorbed quickly by options markets, but identify high proportions in significant and permanent changes in distribution of price returns, option trading activity, short interest in the underlying, and institutional ownership. These results confirm many common assumptions about stock price bubbles. These bubbles are temporally clustered, and tend to occur in periods of positive market development. Martingale defects are rare in market corrections, which indicates that they are a result of overoptimistic speculation.

Suggested Citation

  • Stahl, Philip & Blauth, Jérôme, 2025. "Martingale defects in the volatility surface and bubble conditions in the underlying," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 154110, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    • Handle: RePEc:dar:wpaper:154110
    DOI: 10.1007/s11147-023-09200-x
    Note: for complete metadata visit http://tubiblio.ulb.tu-darmstadt.de/154110/
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    References listed on IDEAS

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