Finance is in a confused mess. The founding fathers of quantitative finance were trapped in a Markovian prison so there were a dizzying array of smart people trying to build hammers looking for finance applications which is reasonable. Even physics has deep problems — I am sure for example that the universe is a scaled four-sphere and quantum mechanics is fooled by randomness and Big Bang never took place and we live in an infinite time steady state universe but at least in physics the empirical tests of complicated models do not have large holes. Not so in finance, where there is this big hole of explaining long memory features being haphazardly sought by extensions of Black-Scholes models with say stochastic volatility a la Heston. Mittag-Leffler waiting times is an empirical fact in all time scales which means that the Markovian models are simply not right; subordination to these waiting times is possible via the work that physicists have done on anomalous diffusion. Time fractional diffusion equations appear whenever Levy processes are subordinated to Mittag-Leffler random times. These should apply to volatility in the stochastic volatility specification.