13.2 MODEL DESCRIPTION

The model provides updated estimates of portfolio volatility using information about changes to the market environment. We describe in this section a slightly modified form of the model outlined in diBartolomeo and Warrick (2005) which updates traditional factor risk estimates using option-implied volatility. This model is extended in the following section with quantified news inputs.

The model is described in two parts. The first is a “basic” statistical factor model. In the second part, factor variance estimates are updated to account for changes in option-implied volatility levels. The asset covariance matrix is re-estimated, using the updated factor variances, to give an improved set of risk estimates.

We construct a statistical factor model applying traditional principal component analysis to extract orthogonal factors.1 For a general factor model, the variance of each asset is given as a linear combination of factor variances and asset-specific variances

image

Sets and indices

k ∈ {1, …, N1} denotes the asset universe;

t ∈ {1, …, T} denotes the time points considered;

i, j ∈ {1, …, F} denotes the factors.

Parameters

Vkt denotes the variance for asset k at time point t ∈ {1,…, T};
βkit denotes factor sensitivity (exposure) to factor i for asset k at time point t;
σit denotes factor variance for factor i at time point t;
ρijt denotes the correlation ...

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