4 research outputs found
Modulated Information Flows in Financial Markets
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 behaviour, 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 analyse by notions of information geometry.Comment: 27 pages, 1 figur