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<p>Put options are known to be priced unusually high in the market, which we refer to as the <i>overpriced put puzzle</i>. This study proposes a quantum model (QM) that can explain such high put option prices as <i>fair</i> prices. Starting from a stochastic differential equation of stock returns, we convert the Fokker–Planck equation into the Schrödinger equation. To model the market force that always draws excess returns back to equilibrium, we specify a diffusion process corresponding to a QM with a delta potential. The results demonstrate that stock returns follow a Laplace distribution and exhibit power law in the tail. We then construct a closed-form solution for European put option pricing, determining that our model better explains the returns of the S&amp;P 500 index and its corresponding put option prices than do geometric Brownian motion-based models. This study has significant implications for investors and risk managers, presenting a model that can potentially improve derivative pricing. Future studies can generalize the model assumptions by introducing asymmetric potential drawing back excess returns to equilibrium.</p>

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A quantum model for the overpriced put puzzle

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年11月28日

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  • Minhyuk Jeong,
  • Biao Yang,
  • Xingjia Zhang,
  • Taeyoung Park,
  • Kwangwon Ahn

摘要

Put options are known to be priced unusually high in the market, which we refer to as the overpriced put puzzle. This study proposes a quantum model (QM) that can explain such high put option prices as fair prices. Starting from a stochastic differential equation of stock returns, we convert the Fokker–Planck equation into the Schrödinger equation. To model the market force that always draws excess returns back to equilibrium, we specify a diffusion process corresponding to a QM with a delta potential. The results demonstrate that stock returns follow a Laplace distribution and exhibit power law in the tail. We then construct a closed-form solution for European put option pricing, determining that our model better explains the returns of the S&P 500 index and its corresponding put option prices than do geometric Brownian motion-based models. This study has significant implications for investors and risk managers, presenting a model that can potentially improve derivative pricing. Future studies can generalize the model assumptions by introducing asymmetric potential drawing back excess returns to equilibrium.