This paper proposes a new model for capturing discontinuities in the underlying financial environment that can lead to abrupt falls, but not necessarily sustained monotonic falls, in asset prices. This notion of price dynamics is consistent with existing understanding of market crashes, which allows for a mix of market responses that are not universally negative. The model may be interpreted as a martingale composed with a randomized drift process that is designed to capture various asymmetric drivers of market sentiment. In particular, the model is capable of generating realistic patterns of price meltdowns and bond yield inflations that constitute major market reversals while not necessarily being always monotonic in form. The recursive and moving window methods developed in Phillips, Shi and Yu (2015a,b; PSY), which were designed to detect exuberance in financial and economic data, are shown to have detective capacity for such meltdowns and expansions. This characteristic of the PSY tests has been noted in earlier empirical studies by the present authors and other researchers but no analytic reasoning has yet been given to explain why methods intended to capture the expansionary phase of a bubble may also detect abrupt and broadly sustained collapses. The model and asymptotic theory developed in the present paper together explain this property of the PSY procedures. The methods are applied to analyse S&P 500 stock prices and sovereign risk in European Union countries over 2001–16 using government bond yields and credit default swap (CDS) premia. A pseudo real-time empirical analysis of these data shows the effectiveness of the monitoring strategy in capturing key events and turning points in market risk assessment.