It is well known that put options are often overpriced, especially in equities. The literature is filled with papers explaining this phenomenon. However, most research still relies on the Black-Scholes-Merton framework, where the underlying asset follows a Geometric Brownian Motion (GBM).
Reference [1] also addresses this question, but it departs from the usual framework by casting the problem into a model rooted in quantum mechanics. Essentially, the new approach proceeds as follows:
- Start with a general stochastic process and solve it by converting the Fokker–Planck (FP) equation into the Schrödinger equation.
- Introduce the delta potential and the Laplace distribution for the stock price.
- Derive a closed-form solution for European put options within the context of quantum mechanics.
The authors pointed out,
To resolve the well-known overpriced put puzzle, we propose an option pricing model inspired by quantum mechanics. Starting from an SDE of stock returns, we convert the FP equation into the Schrödinger equation. We then obtain the PDF of stock returns and a closed-form solution of European options. Our model indicates that S&P 500 index returns follow a Laplace distribution with power-law decay in the tail. We demonstrate that our QM outperforms GBM-based models in describing S&P 500 index returns and their corresponding put option prices. Our results indicate that high put option prices in the market are close to fairness and can be accurately modeled via quantum approaches.
In short, the paper proposes a quantum-mechanics–inspired option pricing model that converts the Fokker–Planck equation into the Schrödinger equation, yielding both the return distribution and a closed-form solution for European options. The model shows that S&P 500 returns follow a Laplace distribution with power-law tails and that quantum methods outperform GBM-based models in explaining return dynamics and put option prices.
This is an interesting formulation of option pricing theory. We note that the framework operates in the physical world rather than under the risk-neutral measure. We believe it may have practical applications in option trading, particularly for traders who rehedge less frequently.
Let us know what you think in the comments below or in the discussion forum.
References
[1] Minhyuk Jeong, Biao Yang, Xingjia Zhang, Taeyoung Park & Kwangwon Ahn, A quantum model for the overpriced put puzzle, Financial Innovation (2025) 11:130
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