Comment: 16 pages, 6 figuresIn 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.