Option Pricing beyond Black-Scholes Model: Quantum Mechanics Approach

Source:
By:Pengpeng Li, Shidong Liang

DOI: https://doi.org/10.30564/jesr.v3i4.2311

Abstract:

Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can take various unexpected market behaviors into account to modify the option pricing. As examples, we present several market forces to analyze their effects on the option pricing. These results provide us two practical applications. One is to be used as a new scheme of option pricing when we can predict some hidden market forces or behaviors emerging. The other implies the existence of some risk premium when some unexpected forces emerge.

References:

[1]F.Black, M.Scholes. The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 1973, 63759. [2]J.C.Hull. Options, futures, and other Derivatives the 10th Edition, Pearson, 2011: 320-323. [3]B. E. Baaquie. Quantum Finance, 2004, 316: 78-115. [4]Lauterbach, Beni. Schultz, Paul, Journal of Finance, 1990, 45: 1181-1209. [5]Scott, Louis O. Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application, 1987, 22: 419-438. [6]Kleinert, H., Korbel, J. Physica. A Statistical Mechanics & Its Applications, 2016, 449: 200-214. [7]Song, Lina, Wang, Weiguo. Abstract & Applied Analysis, 2013, 1-16. [8] Merton, Robert C., J. Financial Economics, 1976, 3: 125-144. [9] Mantegna, Rosario Nunzio, Physica A. Statistical Mechanics & Its Applications, 1991,179: 232. [10] B. E. Baaquie. Quantum Finance, 2004, 316: 76-77. [11] B. E. Baaquie. Quantum Finance, 2004, 316: 73-76. [12] W. Greiner. Quantum mechanics: An introduction, Springer, 2001.