As with other social sciences, economics incorporates a classical worldview which assumes, explicitly or implicitly, that the social world can be modelled as a sort of mechanistic system, governed by deterministic laws of cause and effect (such as supply and demand), and reducible to interactions between independent atoms (people or firms). Quantum social science offers a new paradigm which overturns these basic assumptions; however as always in science or technology, inertia and vested interests in the existing approach means that fundamental change will only be contemplated if the new approach offers dramatic and compelling advantages in some area-a "killer app". This paper argues that the historically reductionist approach of mainstream economic theory has succeeded exactly because it has developed a number of such killer apps, however these have now outlived their usefulness. Quantum social science provides a new approach to the most basic (and long-debated) question of economics, which is the relationship between price and value; and its application in the economic sphere will yield a killer app of a different sort.

In Lewis Carroll's Through the Looking-Glass, the White Queen tells Alice she believes "as many as six impossible things before breakfast." This paper asks the reader to similarly entertain six impossible things about finance: that there can be a non-trivial, surprising, and falsifiable prediction about asset price volatility; that the predicted property would have remained unnoticed for over half a century, despite the fact that this has been an area of intense research interest, and there are tens of models of volatility in use; that any such property could have important and previously unnoticed repercussions for things like option pricing; that the property was hinted at all along by a Cheshire-cat like grin; that the property was predicted by a quantum model, despite being unrelated to subatomic particles; and finally that the property could make something else impossible, namely the continuous-time framework that has dominated quantitative finance since the field was invented.

David Orrell, while writing a book on the history of money, came up with the idea of applying quantum ideas to finance. Without looking at any data, he made a prediction about the behavior of volatility. In the spirit of a true scientist and almost unique in finance, he went on to test this prediction. Here, David and Paul Wilmott discuss what happened next. There is also a request for assistance from the readers. The full paper follows this dialogue.

Q-variance refers to a property of asset price behavior, where the expected variance over a period is related to price change over the same period by a simple quadratic equation, whose only parameter is a base volatility. The property was first predicted using a quantum oscillator model (the q can stand for quadratic, or quantum) but has been demonstrated empirically for a range of asset types. This paper focuses on the consequences of q-variance for topics including asset price modeling, implied volatility, and the estimation of risk. It argues that while classical finance provides a reasonable approximation to some aspects of market behavior, q-variance means that it breaks down when used to estimate volatility, so a new approach is called for.

Perhaps the best-known result from neoclassical economics is the 'law of supply and demand'. This depicts markets using curves of supply and demand that intersect at a unique equilibrium, whose value represents a kind of aggregate market decision about price. However, because it is impossible to separate supply and demand in practice, the model has little in the way of empirical backing. In finance, in contrast, the related question of price impact, where a large transaction results in a changed price, has been widely studied. This paper uses a probabilistic approach to obtain a model of price impact in the context of asset pricing. A model based on classical probability is first used to simulate economic decisions to buy or sell, and a quantum version is then developed that better captures the response of the system to perturbations. The result is then extended to the general question of supply and demand. The formula is used to obtain a relationship between price change and volatility which is illustrated using empirical stock market data, and implications for other areas such as option pricing and real estate are discussed.This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 1)'.

In this extract from Chapter 10 of David Orrell�s book, Quantum Economics and Finance, we turn to the basic economic question of the relationship between supply and demand

The theoretical value of a financial option depends on the assumed probability distribution of price changes of the underlying asset during the life of the option. Although the classical Black-Scholes model assumes that asset returns follow a simple random walk, resulting in a lognormal distribution for the future share price, it has long been known that the actual data is not perfectly Gaussian. Also, the implied volatility, which corresponds to the price actually paid by traders, is seen to depend on the strike price (the so-called volatility smile), which, again, seems inconsistent with classical theory in which the most important parameter, volatility, is a simple constant. A number of alternatives have, therefore, been developed, an early example being the Merton jump-diffusion model from 1976, which assumes that price changes are punctuated by a sequence of abruptjumps. Beginningfrom a simple and easily verified empirical property of market behavior called q-variance, this article develops an option-pricing model in which all price change is caused by jumps, and that provides a good fit to empirical data over different time scales using as parameters only a drift rate and a volatility. In essence, although the lognormal model can be viewed as a zero-order approximation to market dynamics that assumes equilibrium, the new model is a first-order approximation that allows for imbalance but involves no new parameters.

This excerpt from Chapter 8 of David Orrell�s book, Quantum Economics and Finance, looks at some simple examples of quantum games and explores the connections between quantum cognition and quantum game theory.

This excerpt from Chapter 9 of David Orrell�s book, Quantum Economics and Finance, looks at how the paridigmatic example of the quantum oscillator illustrates how physics tackles the problem of "quantization" in complex systems

The antitumor efficacy of an intratumoral injection of a genetically engineered oncolytic vaccinia virus carrying human IL-7 and murine IL-12 genes (hIL-7/mIL-12-VV) was demonstrated in CT26.WT-bearing mice. In the CT26.WT-bearing mouse model, the efficacy of the combination of hIL-7/mIL-12-VV plus the anti-programmed cell death protein (PD)-1 antibody was determined to be correlated with the timing of administration: greater efficacy was observed when hIL-7/mIL-12-VV was administered before the anti-PD-1 agent instead of simultaneous administration. To identify an optimal dosing regimen for first-in-human clinical trials, a multiple model-informed drug-development (MIDD) approach was used through development of a quantitative systems pharmacology (QSP) model and an agent-based model (ABM). All models were built and verified using available literature and preclinical study data. Multiple dosing scenarios were explored using virtual populations by altering the interval between hIL-7/hIL-12-VV and pembrolizumab administration. In contrast with observations from preclinical studies, both the QSP and the ABM models demonstrated no antagonistic effect on the dose-dependent antitumor efficacy of hIL-7/hIL-12-VV by pembrolizumab in simulations of clinical therapy. Based on the MIDD strategy, it was recommended that the highest dose of hIL-7/hIL-12-VV and pembrolizumab should be administered on the same day, but with pembrolizumab administration following hIL-7/hIL-12-VV administration. Multiple different modeling approaches uniquely supported and informed the first-in-human clinical trial design by guiding the optimal dose and regimen selection.

Classical oscillators have long been used to model financial time series, but suffer from the drawback that the underlying system does not behave like a mechanical spring: there are no regular oscillations, and price is not a well-defined mechanical quantity but always has a degree of uncertainty. In recent years a number of authors have attempted to address these problems by basing their models on quantum harmonic oscillators, which always have a non-zero volatility, however the role of other features that are characteristic of quantum systems, such as discrete energy levels, has not been clear. This paper develops a quantum model in which the energy level corresponds to an integer number of transactions. The model is derived by quantizing entropic forces which represent the intentions of buyers and sellers to transact as a function of price. It is shown that the model captures the non-Gaussian nature of financial statistics, and correctly predicts empirical phenomena including the square-root law of price impact, along with its associated variance.

The quantum implied volatility (QIV) model is a minimalistic model of an implied volatility surface. It is derived by assuming that the implied volatility is the volatility which, when used as input to the Black-Scholes model, will produce the correct option price under a previously derived quantum model of asset price. In its base form, the model uses only two parameters to simulate a volatility surface over different strikes and expirations. Results can be improved by adding additional parameters, such as a drift term. The method is illustrated using data from the S&P 500 index, as well as individual stocks.

The publication of the Black-Scholes formula in 1973 appeared for the first time to put the pricing of financial options onto a rational and objective basis. Its adoption transformed the perception of option pricing from a form of gambling to scientific risk management, and led to a huge increase in options trading. However while the formula revolutionised the world of finance, and remains the industry-standard pricing model today, its proof relies on a number of assumptions about price behaviour which are often contested, such as that log prices follow a random walk with constant volatility, and that one can constantly buy or sell stocks and options without incurring transaction fees. This paper presents an alternative approach to option pricing, based on a quantum oscillator model of stock prices. In the quantum model, the bid/ask spread between buy and sell prices is treated as a fundamental measure of uncertainty, and volatility is not constant but exhibits a smile-like dependence on strike. We show how the Black-Scholes model and its assumptions lead to a systematic mispricing of commonly-traded options, while results can be improved by adopting the quantum model.

This excerpt from Chapter 2 of David Orrell�s book, Quantum Economics and Finance, introduces some of the key mathematical tools that are used throughout the book. We�ll start by describing some terms and symbols. Most of them are similar to the terms used in matrix algebra, with the twist that the matrices now involve complex numbers.

A considered response to people who believe quantum economics/finance is too much of a stretch.

From a quantum perspective, the most worrying aspect of the VIX is its mathematical construction.

Abstract Introduction – Murine ANK-101 (mANK-101) is a stable complex composed of a modified murine IL-12 cytokine with aluminum hydroxide at a 1:10 ratio designed for intratumoral delivery to established solid cancers. The objective of this work was to build a preclinical PK/PD/TGI model to gain a better mechanistic understanding of the pharmacology of mANK-101 and potential impact on therapeutic efficacy. Methods - Data were collected from in vivo studies measuring PK, intratumoral immune cells and tumor growth inhibition (TGI) in a CT26 syngeneic mouse model treated with mANK-101. A PK model was derived from Momin et al. [1], the surrogacy potential of immune cells was assessed via a statistical model and subsequently a mathematical model linking immune cell activation to TGI was developed. Results – A two-compartment PK model was established to take into account both the intratumoral depot effect of mANK-101 and the release into the peripheral circulation for mIL12 from the mANK-101 complex. CD8+ T-cell infiltration was found to be a surrogate biomarker for anti-tumor activity and was subsequently used to link PD-TGI. The model was able to capture various doses and schedules of mANK-101 at different starting tumor volumes on therapeutic responses. Conclusions – A PK-PD-TGI model was developed that links the release of mIL12 from mANK-101 to immune cell-activation through to tumor growth inhibition thus providing a causal understanding of the mechanism of action. The model could potentially form the basis of a translational model to assist in designing first-in-man dose and schedule. References:[1] Momin, N., Palmeri, J.R., Lutz, E.A. et al. Maximizing response to intratumoral immunotherapy in mice by tuning local retention. Nat Commun 13, 109 (2022). https://doi.org/10.1038/s41467-021-27390-6 Citation Format: Hitesh Mistry, David Hodson, David Orrell, Sailaja Battula, Leisha A Emens, Howard L Kaufman, Michael M Schmidt, Christophe Chassagnole. Preclinical pharmacokinetic (PK) and tumor growth inhibition (TGI) modeling for mANK-101, an anchored murine interleukin-12 (IL-12) complex for intratumoral administration for solid cancer [abstract]. In: Proceedings of the AACR-NCI-EORTC Virtual International Conference on Molecular Targets and Cancer Therapeutics; 2023 Oct 11-15; Boston, MA. Philadelphia (PA): AACR; Mol Cancer Ther 2023;22(12 Suppl):Abstract nr A141.

The idea that markets are at equilibrium and price changes follow some version of a random walk is key to foundational results from quantitative finance including the Black-Scholes option-pricing model, and is related to other tenets of finance such as market efficiency and the no-arbitrage principle. However it is also inconsistent with the observed price behaviour of both assets and options. Quantum finance offers an alternative approach which captures the dynamic and probabilistic nature of financial transactions, and leads to different predictions of market behaviour. This paper summarises a range of empirical evidence which falsifies the classical equilibrium-based approach including the principles of no-arbitrage and market efficiency; shows how contradictory data have long been downplayed or ignored in the classical literature; and argues that quantum models are better aligned with empirical reality.

While it is really a predictive formula, which estimates option prices based on a probabilistic price distribution, its trick is to present itself as a prescriptive formula (which somehow defines the correct option price � like a mentalist who predicts the future by making it happen. By using it as a calculating device, investors only seem to confirm its predictions. What kind of higher-level voodoo is this?