Quantum Option Pricing and Quantum Finance

In this article, the authors discuss the use of quantum probability, that is, the probability theory of quantum mechanics, for option pricing and for finance in general. The authors discuss the motivations for applying quantum probability to finance. The critical issues are replacing random variables with operators, self-reflexivity of markets, and the existence of incompatible observations. The authors outline quantum probability theory, quantum stochastic processes, and the pricing of options in a quantum context. TOPICS: Options, portfolio theory, portfolio construction Key Findings • Quantum probability theory is a probabilistic theory of observations. Observations can change the system and be incompatible. • Quantum probability offers a more empirically faithful handling of large events and of uncertainty. • A better theory of valuation is offered by quantum probability theory than classical probability theory.

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