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largely local volatility and later stochastic volatility models which explicitly build in time-varying volatility and hence generate fat tails and heteroskedasticity. Like all models they are wrong, but unlike the fractal model, they are useful.
That’s all I have to say about it really. Mandelbrot was not wrong, in fact he was ahead of his time — but his research led in an unproductive direction. The fetishisation of his ideas that has cropped up in the last 10-15 years is weird and I attribute it mostly to people who
have read “fooled by randomness” or “the black swan” once and largely failed to understand them 
I feel like @EmanuelDerman would have a much better take on this than I do!
extreme volatility is more likely during times of volatility is a useful Mandelbrot gem, imo
He also set Taleb loose on the world.
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