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A Theory of Scenario Generation

We show how distributions can be reduced to low-dimensional scenario trees. Applied to intertemporal distributions, the scenarios and their probabilities become time-varying factors. From S&P 500 options, two or three time-varying scenarios suffice to forecast returns, implied variance or skewness on par, or better, than extant multivariate stochastic volatility jump-diffusion models, while reducing the computational effort to fractions of a second.