Asset trading under non-classical ambiguity and heterogeneous beliefs

Khrennikova, Polina; Patra, Sudip

doi:10.1016/j.physa.2019.01.067

Cited by 15 publications

(7 citation statements)

References 59 publications

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“…In practice, the choice of a correct probability measure such that a derivative contract is priced correctly is a subjective and quantitative exercise. In any case, no perfect model exists [42][43][44][45][46]. As a result, participants in financial markets are free to choose whichever probability model they calibrate to market data [47][48][49].…”

Section: Knightian Uncertaintymentioning

confidence: 99%

Learning agents in Black–Scholes financial markets

2020

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Black–Scholes (BS) is a remarkable quotation model for European option pricing in financial markets. Option prices are calculated using an analytical formula whose main inputs are strike (at which price to exercise) and volatility. The BS framework assumes that volatility remains constant across all strikes; however, in practice, it varies. How do traders come to learn these parameters? We introduce natural agent-based models, in which traders update their beliefs about the true implied volatility based on the opinions of other agents. We prove exponentially fast convergence of these opinion dynamics, using techniques from control theory and leader-follower models, thus providing a resolution between theory and market practices. We allow for two different models, one with feedback and one with an unknown leader.

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Section: Knightian Uncertaintymentioning

confidence: 99%

Learning agents in Black–Scholes financial markets

2020

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“…Given the findings of behavioural finance, the QP dynamical framework aims to show the mechanism of bubble formation from the contextual beliefs of agents. The idea of investors' nonclassical beliefs under ambiguity is further developed in [34] whereby the agents can be categorized according to the type of their ambiguity attitude. In line with some earlier works on asset trading under heterogeneous beliefs, agents can behave over-optimistically under informational ambiguity, or show ambiguity aversion through pessimistic beliefs about asset prices.…”

Section: Qp Contributions To Ambiguity Sensitive Behaviour In Economi...mentioning

confidence: 99%

“…In the search for a different theory of probability that could serve as a more general descriptive framework to accommodate context sensitivity of beliefs and preferences, quantum probability (QP) that is based on operational representation of beliefs in a linear vector space, started to be widely explored in decision theory and its applications to psychology, politics, economics, game theory and finance, see some contributions by [1], [5], [6], [10], [38], [11], [23], [26], [25], [33] and [34]. Please also see surveys in [30], [11], [22], [24] and [39].…”

Section: Introductionmentioning

confidence: 99%

A QP Framework: A Contextual Representation of Agents’ Preferences in Investment Choice

Khrennikova

Haven

2020

Data Science for Financial Econometrics

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Contextual decisions and beliefs and their impact upon market outcomes are at the core of research in behavioural finance. We describe some of the notable probabilistic fallacies that underpin investor behaviour and the consequent deviation of asset prices from the rational expectations equilibrium. In real financial markets, the complexity of financial products and the surrounding ambiguity calls for a more general formalization of agents belief formation than offered by the standard probability theory and dynamic models based on classical stochastic processes. The main advantage of quantum probability (QP) is that it can capture contextuality of beliefs through the notion of non-commuting prospect observables. QP has the potential to model myopia in asset return evaluation, as well as inter-asset valuation. Moreover, the interference term of the agents' comparison state can provide a quantitative description of their vacillating ambiguity perception characterized by non-additive beliefs of agents. Some of the implications of non-classicality in beliefs for the composite market outcomes can also be modelled with the aid of QP. As a final step we also discuss the contributions of the growing body of psychological studies that reveal a true (quantum type) contextuality in human preference statistics showing that the classical probability theory is too restrictive to capture the very strong non-classical correlations between preference outcomes and beliefs.

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“…The system of 6 equations must be satisfied by the parameters 0 ≤ α < 1 2 , ρ m , τ m , ρ n , τ n ≥ 0, θ m , φ m , θ n , φ n ∈ . Equations ( 23) and ( 26) are determined by empirical data, (25) and (28) are determined by normalization conditions, while (24) and (27) are determined by the fact that decision-makers who are not sensitive to ambiguity should overall be indifferent between f 1 and f 2 , as well as between f 3 and f 4 . Hence, on average, half respondents are expected to prefer f 1 (f 3 ) and the other half f 2 (f 4 ).…”

Section: Data Representation In the Two-urn Examplementioning

confidence: 99%

Representing Attitudes Towards Ambiguity in Hilbert Space: Foundations and Applications

Sozzo¹

2019

Preprint

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We provide here a general mathematical framework to model attitudes towards ambiguity which uses the formalism of quantum theory as a "purely mathematical formalism, detached from any physical interpretation". We show that the quantum-theoretic framework enables modelling of the Ellsberg paradox, but it also successfully applies to more concrete human decision-making (DM) tests involving financial, managerial and medical decisions. In particular, we provide a faithful mathematical representation of various empirical studies which reveal that attitudes of managers towards uncertainty shift from ambiguity seeking to ambiguity aversion, and viceversa, thus exhibiting hope effects and fear effects in management decisions. The present framework provides a new bold and promising direction towards the development of a unified theory of decisions in the presence of uncertainty.

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Asset trading under non-classical ambiguity and heterogeneous beliefs

Cited by 15 publications

References 59 publications

Learning agents in Black–Scholes financial markets

Learning agents in Black–Scholes financial markets

A QP Framework: A Contextual Representation of Agents’ Preferences in Investment Choice

Representing Attitudes Towards Ambiguity in Hilbert Space: Foundations and Applications

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