A new paradigm based on quantum probability that can model stock markets and price options—and also upends classical quantitative finance. In The Quantum Stock Market, David Orrell combines theory and new empirical findings to argue for a new approach to finance based on quantum probability. The main finding, a property called q-variance, may be unique in finance in that it was discovered as the result of a prediction, affects financial markets in general, has no tunable parameter, and has important consequences for a range of topics including the pricing of financial options. The property, which somehow eluded detection for over a century, has been verified by experts in the field. And the fact that it is incompatible with classical finance—which is perhaps why it went undetected—suggests that the field must be reinvented. Orrell argues for nothing less than a paradigm shift in finance. As with any new work that challenges existing methods the ideas have already received pushback, from leaders in the field of finance to physicists skeptical of applying quantum probability outside its traditional domain. Written in an interdisciplinary style that mixes mathematical equations, data analysis, and informed comments on the field of finance, The Quantum Stock Market should be read by anyone who wants to be on the right side of a paradigm shift.
A new paradigm based on quantum probability that can model stock markets and price options—and also upends classical quantitative finance. In The Quantum Stock Market, David Orrell combines theory and new empirical findings to argue for a new approach to finance based on quantum probability. The main finding, a property called q-variance, may be unique in finance in that it was discovered as the result of a prediction, affects financial markets in general, has no tunable parameter, and has important consequences for a range of topics including the pricing of financial options. The property, which somehow eluded detection for over a century, has been verified by experts in the field. And the fact that it is incompatible with classical finance—which is perhaps why it went undetected—suggests that the field must be reinvented. Orrell argues for nothing less than a paradigm shift in finance. As with any new work that challenges existing methods the ideas have already received pushback, from leaders in the field of finance to physicists skeptical of applying quantum probability outside its traditional domain. Written in an interdisciplinary style that mixes mathematical equations, data analysis, and informed comments on the field of finance, The Quantum Stock Market should be read by anyone who wants to be on the right side of a paradigm shift.
Last twenty years have seen a tremendous growth of the financial mar- kets both in trading volumes and in sophistication of instruments. This ever-increasing complexity of the market structure necessitates use of math- ematically advanced models from the side of market participants. So far, the prevalent paradigm for these models has been the stochastic analysis as a branch of applied mathematics. In the last few years however, there has been an influx of purely physical concepts and methodology, constituting nascent field of econophysics. To what extent this new approach is useful remains, however, an open question. In my bachelor thesis I will focus on one subfield of econophysics, namely quantum finance. First, I will give an overview of both stochastic analysis and the new quantum finance paradigm. Then using the framework of quantum theory and quantum field theory I will construct a model of European stock options. 1
Quantum finance is a new paradigm in financial market operations, based on the principles of quantum computing in solving highly complex problems with efficiency. This chapter covers some basic ideas of quantum finance through its historical context and the role it has played in surmounting the limitations of classical financial models. The chapter commences with the basics, including the need for an introduction to quantum mechanics, qubits, quantum gates, and algorithms that can be applied in financial applications to demonstrate how quantum computing can change finance. We discuss some of those areas where this technology is bound to make an impact: in portfolio optimization, quantum computing considers several combinations of assets at a time; in risk management, improved models will allow for better predictions of market movements; in derivative pricing, the calculations are faster and more accurate; and in fraud detection, it enables one to execute better analysis of transactional data. The advancement of quantum finance is linked to the need to resolve ethical, legal, and technical obstacles while integrating with traditional financial institutions. The financial markets will be a key source of innovation that will drive efficiency, precision, and invention to previously unheard-of heights, given the direction that quantum computing technology is expected to take. Thus, the chapter ends with a call for more study and cooperation to fully grasp quantum finance's transformative potential.
Modern approaches to stock pricing in quantitative finance are typically founded on the 'Black-Scholes model' and the underlying 'random walk hypothesis'. Empirical data indicate that this hypothesis works well in stable situations but, in abrupt transitions such as during an economical crisis, the random walk model fails and alternative descriptions are needed. For this reason, several proposals have been recently forwarded which are based on the formalism of quantum mechanics. In this paper we apply the 'SCoP formalism', elaborated to provide an operational foundation of quantum mechanics, to the stock market. We argue that a stock market is an intrinsically contextual system where agents' decisions globally influence the market system and stocks prices, determining a nonclassical behavior. More specifically, we maintain that a given stock does not generally have a definite value, e.g., a price, but its value is actualized as a consequence of the contextual interactions in the trading process. This contextual influence is responsible of the non-Kolmogorovian quantum-like behavior of the market at a statistical level. Then, we propose a 'sphere model' within our 'hidden measurement formalism' that describes a buying/selling process of a stock and shows that it is intuitively reasonable to assume that the stock has not a definite price until it is traded. This result is relevant in our opinion since it provides a theoretical support to the use of quantum models in 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.
Abstract Finance stands as the most quantitatively advanced branch of the social sciences, yet it is also the most humbling. The mean-variance efficient frontier, the CAPM, arbitrage pricing relations, the Black–Scholes–Merton option formula and the efficient market hypothesis possess unparalleled formal elegance, yet they suffered a broad empirical refutation in the global financial crisis of 2008. Standard models understate tail risk, misinterpret the comovement of assets that are supposed to diversify risk, and presuppose liquidity and rationality — two features that vanish precisely when they are most needed. Behavioural finance has documented an extensive catalogue of cognitive biases, yet it remains a patchwork of isolated effects without a unified calculus of probability. This monograph is the first systematic work to establish quantum finance. It argues that the mathematical formalism of quantum mechanics supplies this missing unified structure: financial states are state vectors in Hilbert space; beliefs and valuations coexist as superposed amplitudes; trading and information disclosure act as measurements that collapse states in accordance with the Born rule; assets and markets are entangled with one another; and path interference generates fat tails and herding, which are inadmissible under classical additive probability. The book comprises six parts and thirty chapters in total. Part I lays the philosophical and formal foundations. Starting from the paradigm crisis, it proceeds through quantum probability and quantum stochastic processes to construct the analytical framework built on three core pillars of quantum finance. Part II develops quantum asset pricing, covering the quantum CAPM, quantum APT, quantum option pricing and the term structure of interest rates. Part III advances quantum risk management, including quantum risk measures, Value-at-Risk (VaR) and expected shortfall, stress testing, credit risk and phase transitions in systemic risk. Part IV addresses quantum portfolios and asset allocation, ranging from the quantum meanvariance frontier, strategic and tactical asset allocation, to factor investing and hedge fund strategies. Part V turns to market microstructure and behavioural finance, examining quantum order flows, marketmaker liquidity, quantum prospect theory and market sentiment. Part VI looks ahead to frontier avenues: quantum computational optimization, quantum machine learning, blockchains, postquantum cryptography and quantuminformed financial regulation. This book rigorously recovers the classical CAPM, efficient market hypothesis and Gaussian risk models as special cases under decoherence limits. It is intended for graduate students and faculty in finance and financial engineering, as well as researchers and practitioners working on asset pricing, risk management, portfolio allocation and financial regulation.
In this paper, we present a quantum version of some portions of Mathematical Finance, including theory of arbitrage, asset pricing, and optional decomposition in financial markets based on finite dimensional quantum probability spaces. As examples, the quantum model of binomial markets is studied. We show that this quantum model ceases to pose the paradox which appears in the classical model of the binomial market. Furthermore, we re-deduce the Cox-Ross-Rubinstein binomial option pricing formula by considering multi-period quantum binomial markets.