Based on historical experience, that assumption cannot be taken for granted when it comes to estimating financial risks. As discussed by Aikman et al (2014), there are at least three reasons for this. 19  All speeches are available online at www.bankofengland.co.uk/speeches  19  First, assigning probabilities is particularly difficult with rare, high-impact events, such as financial crises or the failure of a large financial institution. Degrees of freedom are small in number, historical precedents rarely exact and causal mechanisms imperfectly understood. This means estimated default probabilities, and losses given default, are often highly imprecise. Indeed, that is (one reason) why model-based estimates of the same underlying risks can differ so significantly across banks (BCBS (2014a)). Second, the behaviour of complex, interconnected financial systems can be very sensitive to small changes in initial conditions and shocks. That might be because these systems exhibit multiple equilibria, with path-dependency or hysteresis. Or it may reflect network feedback effects propagating financial contagion. Complex systems exhibit tipping points, with small changes in parameter values capable of moving the system from stability to collapse (Anderson and May (1992), Gai and Kapadia (2010), Gai, Haldane and Kapadia (2011)). In complex webs, the failure of two identical-looking banks can have very different implications for financial system stability. The radical uncertainty in such complex webs generates emergent behaviour which can be near-impossible to predict, model and estimate (Haldane (2016)). Third, because they contain human actors whose beliefs about the future shape their behaviour today, financial systems are particularly prone to instabilities and sunspots.

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