For exercises of bubble detection within this framework see, for example, Obayashi et al. Another approach involves estimating a stochastic volatility model similar to the one studied by Andersen and Piterbarg ( 2007), whose parameter value configuration characterizes the underlying process as either a true martingale or a strict local martingale. ( 4) is finite and characterizes a strict local martingale. If variance increases faster than linearly with level, then the integral in Eq. ( 4), described in “ Financial bubbles and strict local martingales”, provides a testable implication of the SLM hypothesis through the estimation of the variance function of the price process. A diffusion process is a strict local martingale if its volatility increases faster than linearly as its level grows. A key result in this literature states some financial asset price displays a bubble only if it follows a strict local martingale under the equivalent risk-neutral measure. Specifically, the SLM approach circumvents the joint hypothesis hindrance by focusing on purely statistical properties of prices and returns. ( 1988), Camerer and Weigelt ( 1991), and also Nunes and Silva ( 2009) for an application to Brazilian markets. For examples of this literature, see Flood and Hodrick ( 1986), Smith et al. The issue here is that the model can not be independently validated. Because future cash flows are not observable, pinpointing some financial asset’s fundamental value is not straightforward and thus, observed deviations from expected behavior can come either from the real presence of a price bubble or from model misspecification. Camerer ( 1989) reviews this early literature and considers it inconclusive. The SLM approach differs from traditional bubble detecting exercises, in that it avoids the problematic double hypothesis of simultaneously testing a model of market equilibrium and investigating deviations from such equilibrium (what we tend to call bubbles). In this paper, we employ statistical techniques to explore this narrative within the framework of strict local martingale (SLM) financial bubbles, developed for example by Jarrow et al. Narratives about a bubble in Brazilian stocks before the global crash and its subsequent burst are plentiful in specialized media, e.g., Martins ( 2020), with the opinions of some of the biggest financial asset managers on a possible bubble on the Ibovespa. The Ibovespa index tripled its market value between a low point in January 2016 and its maximum in January 2020-by March 12, 2020, half those capital gains had been erased. We also performed a comparative analysis of the patterns found for the Ibovespa with the S&P500 index, spot Brent oil and gold prices.īrazilian stock markets underwent a period of remarkable exuberance between early 2016 and March 2020, only to crash with the global turmoil related to COVID-19 pandemic and falling oil prices. Strict local martingale bubbles are related to a positive relationship between returns and volatility which does not seem present in the data at hand. ![]() Our results are negative towards the presence of a strict local martingale bubble in the Ibovespa index. We first apply a nonparametric method to estimate the volatility function of Ibovespa daily prices, then fit a stochastic volatility model whose parameter values can discriminate the underlying price process as either a true martingale or a strict local martingale. In this paper, we explore this narrative from within the framework of strict local martingale financial bubbles. Narratives about a bubble in Brazilian stocks before the global crash and its subsequent burst are plentiful in specialized media. The Ibovespa index tripled its market value between a low point in January 2016 and its maximum in January 2020-by March 12, half those gains had been erased. Brazilian stock markets underwent a period of remarkable exuberance between early 2016 and March 2020, only to crash with the global turmoil related to health worries and oil prices.
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