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Modulated Information Flows in Financial Markets

Hoyle, E; Macrina, A; Mengütürk, LA; (2020) Modulated Information Flows in Financial Markets. International Journal of Theoretical and Applied Finance , 23 (4) , Article 2050026. 10.1142/S0219024920500260.

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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.

Type: Article
Title: Modulated Information Flows in Financial Markets
DOI: 10.1142/S0219024920500260
Publisher version: https://doi.org/10.1142/S0219024920500260
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Information-based theory, jump-diffusion, point processes, stochastic volatility, asymmetric information, f-divergencies
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10063706
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