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Quantum effects in an expanded Black-Scholes model.

Anantya Bhatnagar¹, Dimitri D Vvedensky¹

¹The Blackett Laboratory, Imperial College London, London, SW7 2AZ UK.

The European Physical Journal. B

|September 5, 2022

Summary

This summary is machine-generated.

This study reveals limitations in the Black-Scholes model by comparing theoretical and actual option prices. An expanded model incorporating a non-classical process better explains market behavior and option pricing.

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Area of Science:

Quantitative Finance
Financial Modeling
Market Analysis

Background:

The classical Black-Scholes model has limitations in accurately pricing European call options.
Empirical evidence shows persistent discrepancies between Black-Scholes calculated prices and actual historical option prices.

Purpose of the Study:

To examine the limitations of the Black-Scholes model using S&P 500 stock data.
To introduce and validate an expanded option pricing model that accounts for unobservable information.

Main Methods:

Comparison of calculated Black-Scholes option prices with actual historical prices for S&P 500 stocks.
Application of an expanded model incorporating an additional pseudo-Wiener process.
Analysis of a commutation relation analogous to quantum field theory.

Main Results:

Persistent differences between classical model prices and actual prices were observed.
The expanded model, using a complex quantity's norm, demonstrated improved pricing accuracy.
The imaginary part of the complex quantity effectively compensated for pricing disparities.

Conclusions:

The classical Black-Scholes model's limitations necessitate an expanded framework.
Market data supports the influence of a non-classical, non-commuting process on security pricing.
The proposed model offers a more accurate approach to European call option valuation.