  We consider calculation of capital requirements when the underlying economic
scenarios are determined by simulatable risk factors. In the respective nested
simulation framework, the goal is to estimate portfolio tail risk, quantified
via VaR or TVaR of a given collection of future economic scenarios representing
factor levels at the risk horizon. Traditionally, evaluating portfolio losses
of an outer scenario is done by computing a conditional expectation via
inner-level Monte Carlo and is computationally expensive. We introduce several
inter-related machine learning techniques to speed up this computation, in
particular by properly accounting for the simulation noise. Our main workhorse
is an advanced Gaussian Process (GP) regression approach which uses
nonparametric spatial modeling to efficiently learn the relationship between
the stochastic factors defining scenarios and corresponding portfolio value.
Leveraging this emulator, we develop sequential algorithms that adaptively
allocate inner simulation budgets to target the quantile region. The GP
framework also yields better uncertainty quantification for the resulting
VaR/TVaR estimators that reduces bias and variance compared to existing
methods. We illustrate the proposed strategies with two case-studies in two and
six dimensions.
