Modulated Information Flows in Financial Markets

TL;DR

This paper models continuous-time information flows in financial markets using stochastic processes that switch on and off, leading to jump-diffusion dynamics and enabling novel option pricing and informational advantage analysis.

Contribution

It introduces a framework for modeling information flows with random switching, deriving jump-diffusion dynamics, and providing an information-based approach to option pricing and market advantage.

Findings

Derivation of jump-diffusion dynamics for information flows.

Option pricing expressed as a weighted sum over state configurations.

Quantification of asymmetric informational advantage among agents.

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 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.