A quantum model for the overpriced put puzzle

Minhyuk Jeong (), Biao Yang (), Xingjia Zhang (), Taeyoung Park () and Kwangwon Ahn ()
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Minhyuk Jeong: Yonsei University, Department of Industrial Engineering
Biao Yang: Shanghai Jiao Tong University, Antai College of Economics and Management
Xingjia Zhang: CITIC Securities Company Limited
Taeyoung Park: Yonsei University, Department of Applied Statistics
Kwangwon Ahn: Yonsei University, Department of Industrial Engineering

Financial Innovation, 2025, vol. 11, issue 1, 1-23

Abstract: Abstract 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.

Keywords: Put option pricing; Delta potential; Fokker–Planck equation; Schrödinger equation (search for similar items in EconPapers)
JEL-codes: C65 G12 G13 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1186/s40854-025-00869-7

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