Why do prices jump?

After years of investigation, we still aren’t sure, says Jean-Philippe Bouchaud

It is well known that the distribution of price changes is heavy-tailed, with extreme events – so-called ‘jumps’ – occurring with far greater frequency than the Black-Scholes, Gaussian framework would predict. Even the most sophisticated path-dependent, stochastic volatility models struggle to account for such tails. To put this into context: individual stocks tend to experience moves larger than