## 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

*Sets and indices*

*k* ∈ {1, …, *N*_{1}} denotes the asset universe;

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

*i*, *j* ∈ {1, …, *F*} denotes the factors.

*Parameters*

V_{kt} |
denotes the variance for asset k at time point t ∈ {1,…, T}; |

β_{kit} |
denotes factor sensitivity (exposure) to factor i for asset k at time point t; |

σ_{it} |
denotes factor variance for factor i at time point t; |

ρ_{ijt} |
denotes the correlation ... |

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