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

Author

Listed:
  • Philip Stahl

    (Technische Universität Darmstadt
    Deka Investment GmbH
    IQAM Research GmbH)

  • Jérôme Blauth

    (Deka Investment GmbH
    IQAM Research GmbH)

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

  • Philip Stahl & Jérôme Blauth, 2024. "Martingale defects in the volatility surface and bubble conditions in the underlying," Review of Derivatives Research, Springer, vol. 27(1), pages 85-111, April.
    • Handle: RePEc:kap:revdev:v:27:y:2024:i:1:d:10.1007_s11147-023-09200-x
    DOI: 10.1007/s11147-023-09200-x
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