Horizon scaling

Why a fixed grid encodes a two week liquidation horizon.

The width of the grid determines whether the system is usable. What must be covered is the distance the market can travel before a liquidator can close the position, so the shock is derived from the liquidation horizon and the volatility of the underlying rather than chosen as a round percentage.

u_{\max} = κ σ \sqrt{\frac{h}{365}}

At σ = 0.42, h = 2 days and κ = 3 this gives 9.33%.

Inverting the relation

A system using a fixed ±25% shock is asserting a horizon:

h = 365 {(\frac{u_{\max}}{κ σ})}^{2} = 365 {(\frac{0.25}{3 \times 0.42})}^{2} \approx 14.4

Principal result

A fixed ±25% grid at single name volatility encodes an implied liquidation horizon of roughly two weeks. Under that assumption every long option is stressed to near zero and the system concludes, correctly given its own premise, that no option has collateral value. The conclusion is an artefact of the grid width, not a property of options. This is the difference between an engine that lends nothing and one that advances 65.7% against the same position.

What the horizon assumes

That a liquidator can exit within h days at a price near the mark. In a dislocation the wings do not trade at any price. No liquidity term is present in the model, and advance rates on thin strikes should be lower than the engine currently sets them.