Fitting Accumulated Stock Returns with Tempered Skew t-Distribution (opens in new tab)

We analyze distributions of historic S&P500 multi-day returns, for the number of days of accumulation from 20 to 120. With the increase of the number of days of accumulation, we observe clear tempering of power-law tails toward a seemingly finite value. To explain this phenomenon, we employ a model that produces a "capped Inverse Gamma" stationary (steady-state) distribution for stochastic volatility which, in turn, produces a "tempered Studen...