A Quantum Walk Model of Financial Options

Orrell, David

doi:10.1002/wilm.10918

Cited by 11 publications

(6 citation statements)

References 30 publications

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“…A transaction behaves like a measurement on the quantum walk state, which forces the coherent superposition into a particular state. Some ways of inserting and tuning the level of decoherence are discussed by Orrell (2021), noting in particular that if the quantum walk is measured at every time increment, decoherence is complete and the quantum walk collapses to the classical version.…”

Section: Random Walks Stock Prices and Quantum Walksmentioning

confidence: 99%

Quantum Financial Modeling on Noisy Intermediate-Scale Quantum Hardware: Random Walks Using Approximate Quantum Counting

Widdows,

Bhattacharyya

2024

Quantum Economics and Finance

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Quantum computers are expected to contribute more efficient and accurate ways of modeling economic processes. Quantum hardware is currently available at a relatively small scale, but effective algorithms are limited by the number of logic gates that can be used, before noise from gate inaccuracies tends to dominate results. Some theoretical algorithms that have been proposed and studied for years do not perform well yet on quantum hardware in practice. This encourages the development of suitable alternative algorithms that play similar roles in limited contexts. This paper implements this strategy in the case of quantum counting, which is used as a component for keeping track of position in a quantum walk, which is used as a model for simulating asset prices over time. We introduce quantum approximate counting circuits that use far fewer 2-qubit entangling gates than traditional quantum counting that relies on binary positional encoding. The robustness of these circuits to noise is demonstrated. While this paper is mainly about robust simplified quantum circuit designs, we compare some aspects of the results with price change distributions from stock indices, and compare the behavior of circuits with and without mid-measurement to trends in the housing market.

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Section: Random Walks Stock Prices and Quantum Walksmentioning

confidence: 99%

Quantum Financial Modeling on Noisy Intermediate-Scale Quantum Hardware: Random Walks Using Approximate Quantum Counting

Widdows,

Bhattacharyya

2024

Quantum Economics and Finance

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“…When the results are merged using a fitting routine, the effect is to produce an apparent skew, so the minimum volatility is displaced to the right. Also, while the approach here assumes that returns are unimodal, investor perceptions of the future may follow a different pattern, and in fact there is evidence that a better model can be obtained using a bimodal quantum walk distribution which affects the shape of the volatility smile and introduces a dependence on expiration date (Orrell, 2021). Another type of distortion is due to the assumption in the Black-Scholes model that the growth rate should be equal to the risk-free rate, which as seen below also tends to shift the volatility smile to the right.…”

Section: What Are You Implying?mentioning

confidence: 99%

Quantum Uncertainty and the Black-Scholes Formula

Orrell

2024

Quantum Economics and Finance

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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.

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“…Because the oscillator model is inherently probabilistic, it can be used to model market phenomena such as the pricing and volume of financial options (Orrell, 2021a;Anonymous, 2021) for which empirical data is readily available. Another difference between quantum and classical oscillators is that the former features discrete energy levels.…”

Section: Question Order a Yes A No B Yes B Nomentioning

confidence: 99%

Quantum Propensity in Economics

Orrell¹,

Houshmand²

2022

Front. Artif. Intell.

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This paper describes an approach to economics that is inspired by quantum computing, and is motivated by the need to develop a consistent quantum mathematical framework for economics. The traditional neoclassical approach assumes that rational utility-optimisers drive market prices to a stable equilibrium, subject to external perturbations or market failures. While this approach has been highly influential, it has come under increasing criticism following the financial crisis of 2007/8. The quantum approach, in contrast, is inherently probabilistic and dynamic. Decision-makers are described, not by a utility function, but by a propensity function which specifies the probability of transacting. We show how a number of cognitive phenomena such as preference reversal and the disjunction effect can be modelled by using a simple quantum circuit to generate an appropriate propensity function. Conversely, a general propensity function can be quantized, via an entropic force, to incorporate effects such as interference and entanglement that characterise human decision-making. Applications to some common problems and topics in economics and finance, including the use of quantum artificial intelligence, are discussed.

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A Quantum Walk Model of Financial Options

Cited by 11 publications

References 30 publications

Quantum Financial Modeling on Noisy Intermediate-Scale Quantum Hardware: Random Walks Using Approximate Quantum Counting

Quantum Financial Modeling on Noisy Intermediate-Scale Quantum Hardware: Random Walks Using Approximate Quantum Counting

Quantum Uncertainty and the Black-Scholes Formula

Quantum Propensity in Economics

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