Liquidity Adjusted Value at Risk (L-VaR)

The comprehensive benchmark capturing the total cost of trading, defined as the difference between the decision price and the final execution price. It decomposes into explicit costs (commissions, fees) and implicit costs (delay, market impact). L-VaR extends this concept by integrating the shortfall's tail risk into a pre-trade risk framework.

A foundational optimal execution framework that formalizes the trade-off between market impact cost and timing risk. It models price dynamics with permanent and temporary impact components, providing the mathematical basis for many L-VaR calculations by optimizing the liquidation schedule to minimize the combined cost-and-risk objective.

The rate at which the temporary price distortion caused by an executed trade dissipates. This parameter is critical for L-VaR because it determines the resilience of the order book. A slow decay implies that a liquidating trader will continue to depress the price for subsequent child orders, increasing the total liquidity-adjusted risk.

An empirical market microstructure model stating that the expected price impact of a trade is proportional to the square root of the trade size relative to volume. L-VaR models often incorporate this non-linear relationship to scale the liquidity surcharge for larger positions, recognizing that doubling the position size does not simply double the liquidation cost.

A measure of market illiquidity representing the linear relationship between order flow imbalance and the resulting permanent price change. In the L-VaR context, a high lambda indicates that trades convey significant private information, leading to a steep permanent impact that must be priced into the liquidation horizon's risk assessment.

The actual cost of a round-trip trade, calculated as twice the absolute difference between the execution price and the mid-price at the time of the trade. L-VaR uses the effective spread to calibrate the immediate liquidity cost component, distinguishing between the cost of crossing the spread and the subsequent adverse price movement.