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Quantitative Finance · शब्दावली

Parametric value at risk क्या है?

Definition 21.5 Rates, Credit, XVA and Risk · अध्याय 21 — Market-Risk Measures

Parametric value at risk (delta-normal) linearises the P&L in the factor changes, ΔV≈δ⊤x\Delta V\approx\delta^\top x, assumes xx normal with covariance Σ\Sigma, and gives VaRα=zαδ⊤Σδ\mathrm{VaR}_\alpha = z_\alpha\sqrt{\delta^\top\Sigma\delta}. With exponentially weighted covariances (Σt=λΣt−1+(1−λ)xtxt⊤\Sigma_t = \lambda\Sigma_{t-1}+(1-\lambda)x_tx_t^\top, λ=0.94\lambda = 0.94 for daily data in RiskMetrics) it follows volatility quickly.

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