Modulated Information Flows in Financial Markets

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.

Reinforcement-learning-based optimal trading in a simulated futures market with heterogeneous agents

“…activation and deactivation) of individual signals-is beyond the scope of this work. However, interested readers are referred to Hoyle et al 7 for a detailed yet theoretically demanding exposition. In summary, the dynamics of the conditional expectation process is found to be a jump-diffusion where jumps arise naturally from the activation and deactivation of different individual signals over the trading horizon.…”

“…Similar to Aydin 6 and Hoyle et al, 7 we now introduce an F i t -adapted stopping time u ij t which keeps track of the most recent time up to the auction time t and there was a trade interaction between agents i and j, that is as follows:…”

“…In this paper, we aim to extend the signal-based framework introduced in Brody et al, 1 first, toward an agent network where interactions (such as learning and trading) can take place and, second, by formulating a dynamic programming approach based on reinforcement learning (RL) for finding the optimal strategy to exploit differential information (see also [2][3][4][5][6][7] ). The validation of the algorithm is performed through a numerical example based on a network Department of Industrial Engineering, Istinye University, Turkey including a given number of risk-neutral agents that trade futures on a random terminal payoff with known deadline.…”

Pricing with Variance Gamma Information

“…The resulting models are finely tuned to the structures of the assets that they represent, and therefore offer scope for a useful approach to financial risk management. In previous work on information-based asset pricing, where precise definitions can be found that expand upon the ideas summarized above, such models have been constructed using Brownian bridge information processes (Brody et al (2007(Brody et al ( , 2008a(Brody et al ( , 2009(Brody et al ( , 2010(Brody et al ( , 2011, Filipović et al (2012), Hughston and Macrina (2012), Macrina (2006), Mengütürk (2013), Rutkowski and Yu (2007)), gamma bridge information processes (Brody et al (2008b)), Lévy random bridge information processes (Hoyle (2010), Hoyle et al (2011Hoyle et al ( , 2015Hoyle et al ( , 2020, Mengütürk (2018)) and Markov bridge information processes (Macrina (2019)). In what follows we present a new model for the market filtration, based on the variance-gamma process.…”

Pricing with Variance Gamma Information

“…The resulting models are finely tuned to the structures of the assets that they represent, and therefore offer scope for a useful approach to financial risk management. In previous work on information-based asset pricing, where precise definitions can be found that expand upon the ideas summarized above, such models have been constructed using Brownian bridge information processes (Brody et al (2007(Brody et al ( , 2008a(Brody et al ( , 2009(Brody et al ( , 2010(Brody et al ( , 2011, Filipović et al (2012), Hughston and Macrina (2012), Macrina (2006), Mengütürk (2013), Rutkowski and Yu (2007)), gamma bridge information processes (Brody et al (2008b)), Lévy random bridge information processes (Hoyle (2010), Hoyle et al (2011Hoyle et al ( , 2015Hoyle et al ( , 2020, Mengütürk (2018)) and Markov bridge information processes (Macrina (2019)). In what follows we present a new model for the market filtration, based on the variance-gamma process.…”