Modeling Prices from Speculative Markets: Bursting Bubbles or Deflating Balloons?

Speculative markets may be characterized by sharp falls after a slow build up. Sometimes the converse happens. We suggest a number of mechanisms that are able to produce this kind of behaviour and we demonstrate their plausibility by simulation. The models are then fitted to daily data on Bitcoin. In constructing these models we show that it is essential to take account of volatility and non-normality. We also investigate the possibility of a dynamic tail index. The conclusion, at least for Bitcoin, is that speculative markets are more likely to behave like balloons than bubbles. In other words, there is rapid inflation followed by a slow decline.