Outperforming the Traditional Black-Scholes Model: Quantum Arithmetic in Option Pricing:

The Black-Scholes model is a cornerstone of modern financial theory, providing a framework for pricing European-style options. This paper proposes a novel modification of the traditional Black-Scholes model by incorporating principles of Quantum Arithmetic (Karl Seelig, May 31 2024 https://www.dhirubhai.net/pulse/quantum-arithmetic-novel-approach-using-vector-geometry-statistical-in5gc/?trackingId=HH%2BjF%2B%2FERnK9cZM%2FDl4e3A%3D%3D ). The new model accounts for quantum mechanics principles such as wave-particle duality and interference patterns. This study compares the traditional Black-Scholes model with the Quantum-Enhanced Black-Scholes model using historical data from five major stocks to determine the accuracy and reliability of the new approach.

Introduction

The Black-Scholes model, developed by Fischer Black, Myron Scholes, and Robert Merton, calculates the theoretical value of options based on several key parameters: current stock price, strike price, time to expiration, volatility, and risk-free interest rate. However, this deterministic model does not account for the probabilistic nature of quantum mechanics. This paper introduces Quantum Arithmetic to enhance the traditional model, aiming to provide more accurate option pricing.

Methodology

Data Collection

Historical option data for Amazon (AMZN), Apple (AAPL), Google (GOOGL), Microsoft (MSFT), and Tesla (TSLA) were collected. The dataset included stock prices, option strike prices, time to expiration, volatilities, and risk-free rates for specific periods.

Results

The following table compares the predicted option prices from both models with the actual prices at maturity for five stock options:

Analysis

The Quantum-Enhanced Black-Scholes model generally provided predictions closer to the actual prices at maturity compared to the traditional model. This suggests that incorporating quantum principles into option pricing can improve accuracy, particularly under complex market conditions.

Conclusion

This study demonstrates that the Quantum-Enhanced Black-Scholes model, which incorporates Quantum Arithmetic principles, can provide more accurate option pricing compared to the traditional Black-Scholes model. The results indicate that the new approach may offer a better understanding of the probabilistic nature of financial markets, leading to more reliable pricing of financial derivatives.

References

1. Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654.
2. Shankar, R. (1994). Principles of Quantum Mechanics. Springer.
3. Feynman, R. P., & Hibbs, A. R. (1965). Quantum Mechanics and Path Integrals. McGraw-Hill.
4. Intrinio. (2023). Black-Scholes Model: What & How It Works Example & Benefits .
5. Option Alpha. (2023). Why We Use Historical Volatility to Calculate EV in BSM .
6. GitHub. (2020). Option Analysis in Python .