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Abstract We ask whether empirical finance market data (Financial Stress Index, swap and equity, emerging and developed, corporate and government, short and long maturity), with their recently observed alternations between calm periods and financial turmoil, could be described by a low-dimensional deterministic model, or whether this requests a stochastic approach. We find that a deterministic model performs at least as well as one of the best stochastic models, but may offer additional insight into the essential mechanisms that drive financial markets.