MODULATED INFORMATION FLOWS IN FINANCIAL MARKETS

Edward Hoyle (), Andrea Macrina and Levent Ali Mengütürk ()
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Edward Hoyle: AHL Partners LLP, Man Group plc, London EC4R 3AD, United Kingdom
Andrea Macrina: Department of Mathematics, University College London, London WC1E 6BT, United Kingdom†African Institute of Financial Markets and Risk Management, University of Cape Town, Rondebosch 7701, South Africa
Levent Ali Mengütürk: Department of Mathematics, University College London, London WC1E 6BT, United Kingdom

International Journal of Theoretical and Applied Finance (IJTAF), 2020, vol. 23, issue 04, 1-35

Abstract: We model continuous-time information flows generated by a number of information sources that switch on and off at random times. By modulating a multi-dimensional Lévy random bridge over a random point field, our framework relates the discovery of relevant new information sources to jumps in conditional expectation martingales. In the canonical Brownian random bridge case, we show that the underlying measure-valued process follows jump-diffusion dynamics, where the jumps are governed by information switches. The dynamic representation gives rise to a set of stochastically-linked Brownian motions on random time intervals that capture evolving information states, as well as to a state-dependent stochastic volatility evolution with jumps. The nature of information flows usually exhibits complex behavior, however, we maintain analytic tractability by introducing what we term the effective and complementary information processes, which dynamically incorporate active and inactive information, respectively. As an application, we price a financial vanilla option, which we prove is expressed by a weighted sum of option values based on the possible state configurations at expiry. This result may be viewed as an information-based analogue of Merton’s option price, but where jump-diffusion arises endogenously. The proposed information flows also lend themselves to the quantification of asymmetric informational advantage among competitive agents, a feature we analyze by notions of information geometry.

Keywords: Information-based theory; jump-diffusion; point processes; stochastic volatility; asymmetric information; f-divergencies (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0219024920500260

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