Journal article

Modulated information flows in financial markets


Research Areas

Publication Details

Author list: Hoyle E, Macrina A, Mengütürk LA

Publisher: World Scientific Publishing

Publication year: 2020

Journal: International Journal of Theoretical and Applied Finance

Volume number: 23

Issue number: 4

Start page: 1

End page: 35

Total number of pages: 35

ISSN: 0219-0249

eISSN: 1793-6322

URL: https://www.worldscientific.com/


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
L´evy 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 jumpdiffusion
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.


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Keywords

information goods, Stochastics


Last updated on 2021-05-03 at 23:14