How is market impact incorporated into LVaR for large positions?

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AcadiFi · Accepted Answer

Market impact LVaR recognizes that selling a large position moves the price adversely. The common approach uses a power-law or linear-impact model: price_impact = lambda * (Q/ADV)^alpha * sigma, where Q is quantity sold, ADV is average daily volume, sigma is daily vol, lambda and alpha are calibrated parameters. Simplified linear formulation: LVaR_total = VaR + spread_cost + market_impact_cost. Impact cost = 0.5 * P * k_impact * (Q/ADV) * sigma, where k_impact ~ 0.5-1.0. Example: Redlands Telecom position $15M, ADV $30M (position is 50% of ADV), daily vol 2.1%, k_impact=0.8. Impact cost = 0.5 * 15,000,000 * 0.8 * 0.50 * 0.021 = $63,000. Combined with spread cost $40,000 and price VaR $280,000: LVaR = 280,000 + 40,000 + 63,000 = $383,000. Alternatively, multi-day liquidation: if optimal liquidation takes T days selling Q/T per day, impact shrinks but price-risk VaR grows proportionally to sqrt(T). Optimal T balances the two. This is the Almgren-Chriss framework — minimize total execution cost + timing risk. ```mermaid flowchart TD A[Large position] --> B{Liquidate fast?} B -->|Yes| C[High impact,
low timing risk] B -->|Slow| D[Low impact,
high timing risk] C --> E[Optimal T] D --> E ``` For regulatory capital, Basel liquidity-horizon rules set liquidation periods by asset class rather than optimizing, which can over- or under-state impact depending on positioning.

How is market impact incorporated into LVaR for large positions?

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