Dynamics of a Binary Option Market with Exogenous Information and Price Sensitivity

TL;DR

This paper models binary option markets with external information, analyzing price dynamics and sensitivity, revealing convergence under constant info and effects of sensitivity on price lag, with links to neural networks.

Contribution

It introduces a continuous model of binary option markets with exogenous info, analyzing stability, sensitivity effects, and connections to neural networks, which is novel in market modeling.

Findings

Prices always converge with constant exogenous information.

Price sensitivity influences the lag between prices and information.

Binary markets are equivalent to simple recurrent neural networks.

Abstract

In this paper, we derive and analyze a continuous of a binary option market with exogenous information. The resulting non-linear system has a discontinuous right hand side, which can be analyzed using zero-dimensional Filippov surfaces. Under general assumptions on purchasing rules, we show that when exogenous information is constant in the binary asset market, the price always converges. We then investigate market prices in the case of changing information, showing empirically that price sensitivity has a strong effect on price lag vs. information. We conclude with open questions on general $n$-ary option markets. As a by-product of the analysis, we show that these markets are equivalent to a simple recurrent neural network, helping to explain some of the predictive power associated with prediction markets, which are usually designed as $n$-ary option markets.