A discussion on embedding the Black–Scholes option pricing model in a quantum physics setting

In this paper we consider the implications of embedding the Black–Scholes option pricing model within a quantum physical setting. The option price is considered to be a state function and a potential function is found which allows the option price to satisfy the Schrödinger differential equation. Once this arbitrage-free potential function is obtained, we argue for the construction of a so-called ‘arbitrage’ potential function. This functional is instrumental in determining the existence of a ‘financial’ state function. We show the existence of an arbitrage-free price when the potential function converges to one. The existence of arbitrage hinges on the non-zero value of the Planck constant. This constant is then linked to a parameter which regulates the probability of occurence of strategy paths. We call this parameter the ‘belief’ parameter. We argue that it is the belief parameter which may indeed proxy arbitrage. The outcome of this paper shows that the Black–Scholes model can be captured within a quantum physical setting and that the advantages of doing so may indeed provide for a first step to include arbitrage in a natural way in an otherwise arbitrage free model.