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Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement
Risk Management · Submitted 14 Oct 2017
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The GP framework also yields better uncertainty quantification for the resulting VaR/TVaR estimators that reduces bias and variance compared to existing methods.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider calculation of capital requirements when the underlying economic scenarios are determined by simulatable risk factors. | background 0.96 | 0.32 | 0.03 | asserted 0.74 |
| s1 | 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. | background 0.98 | 0.14 | 0.05 | asserted 0.99 |
| s2 | Traditionally, evaluating portfolio losses of an outer scenario is done by computing a conditional expectation via inner-level Monte Carlo and is computationally expensive. | background 0.93 | 0.05 | 0.02 | asserted 1.00 |
| s3 | We introduce several inter-related machine learning techniques to speed up this computation, in particular by properly accounting for the simulation noise. | contribution 0.98 | 0.92 | 0.12 | asserted 1.00 |
| s4 | 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. | method 0.87 | 0.91 | 0.23 | asserted 1.00 |
| s5 | Leveraging this emulator, we develop sequential algorithms that adaptively allocate inner simulation budgets to target the quantile region. | method 0.88 | 0.94 | 0.10 | asserted 1.00 |
| s6 | The GP framework also yields better uncertainty quantification for the resulting VaR/TVaR estimators that reduces bias and variance compared to existing methods. | result 0.93 | 0.89 | 0.33 | asserted 1.00 |
| s7 | We illustrate the proposed strategies with two case-studies in two and six dimensions. | contribution 0.58 | 0.93 | 0.05 | asserted 1.00 |
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Original abstract
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.
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What it cites · 5 sentences without a confident label
Contests 1 paper
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Existing approaches in the simulation literature fall short for this application, whether it be assuming the level ($_$) is known [ref] and/or non-noisy outputs [ref] , using a non sequential algorithm [ref] , or not using a spatial model for smoothing [ref] .
Sequential design of experiments for estimating percentiles of black-box functions · Conclusion · contest 0.81
Uses the method or tool of 1 paper
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To overcome this limitation, we use an extended GP model [ref] that jointly models the response mean $z↦f(z)$ and (log)-variance $z ↦logτ^2(z)$.
Practical heteroskedastic Gaussian process modeling for large simulation experiments · Intrinsic Variance · 0.97
Cites as background 2 papers
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More recently, emulation was adapted to the Monte Carlo setting where $f(z)$ is only noisily observed: see e.g. [ref] .
Practical heteroskedastic Gaussian process modeling for large simulation experiments · Introduction · 0.90
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More broadly, our localized objective resembles three inter-related formulations in the engineering reliability literature that target $f(z)$ in relation to a given level or threshold $L$: * Contour-finding: determining the set ${z : f(z) ∈(L-ε, L+ε)}$, $ε$ small, cf. [ref] ;
Sequential design of experiments for estimating percentiles of black-box functions · Introduction · 0.85
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