Sparse economic scenarios
54 Pages Posted: 22 Mar 2019 Last revised: 6 Aug 2021
Date Written: March 22, 2019
We propose a low-dimensional scenario tree representation of distributions of financial asset prices. For intertemporal distributions, the scenarios and their martingale probabilities become time-varying persistent factors that naturally accommodate a nonparametric model for the corresponding physical probabilities. In the S&P 500 index market, two to four time-varying scenarios generate sizable out-of-sample predictability. Together, the low-dimensional physical and risk-neutral conditional distributions yield the simplest possible mechanism describing how risk-neutral variance, expected returns, and the variance risk premium are linked. Multivariate low-dimensional scenarios identify cluster risk in its most parsimonious form.
Keywords: options, dimension reduction, factor model, moment problem, scenario analysis, machine learning, RKHS
JEL Classification: G13, G02, G17, C02, C14, C46, C52, C53
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