# Non-linear Black-Scholes Option Pricing Model based on Quantum Dynamics

### Marcin Wróblewski, Andrzej Myślinski

#### 2022

#### Abstract

This paper is concerned with the option pricing based on an extended non-linear Black-Scholes model. In literature, non-linear Black-Scholes models are formulated assuming the stochastic asset price volatility, volatile risk-free interest rate or the occurrence of the transaction costs. Since these assumptions are matching better the real market conditions, these models are regarded to be more accurate in option pricing than linear Black- Scholes model. In this paper the option pricing model is derived from non-linear Schrödinger equation. This equation governs the movement of quantum particles which is similar to the volatility of stock prices. The nonlinear Schrödinger equation with external potential terms is formulated. The non-linear Black-Scholes option pricing model is formulated using the transformation of the non-linear Schrödinger equation from complex Hilbert to real Euclidean space. The developed model has been used to predict European call options price based on WIG20 stock prices. The model parameters have been estimated based on real market data. The method of lines has been used to solve numerically the non-linear option pricing model. The model parameters have been estimated based on real market data. Numerical results are provided and discussed. The obtained results confirm high accuracy of the proposed non-linear model.

Download#### Paper Citation

#### in Harvard Style

Wróblewski M. and Myślinski A. (2022). **Non-linear Black-Scholes Option Pricing Model based on Quantum Dynamics**. In *Proceedings of the 7th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,* ISBN 978-989-758-565-4, pages 26-35. DOI: 10.5220/0011066000003197

#### in Bibtex Style

@conference{complexis22,

author={Marcin Wróblewski and Andrzej Myślinski},

title={Non-linear Black-Scholes Option Pricing Model based on Quantum Dynamics},

booktitle={Proceedings of the 7th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,},

year={2022},

pages={26-35},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0011066000003197},

isbn={978-989-758-565-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 7th International Conference on Complexity, Future Information Systems and Risk - Volume 1: COMPLEXIS,

TI - Non-linear Black-Scholes Option Pricing Model based on Quantum Dynamics

SN - 978-989-758-565-4

AU - Wróblewski M.

AU - Myślinski A.

PY - 2022

SP - 26

EP - 35

DO - 10.5220/0011066000003197