Why Cascading
Risk Models Fail

Current cascading risk models assume linear propagation. This paper sets out why they systematically underestimate tail losses, and proposes the Abgalis Engine cross-domain transmission alternative.

The vocabulary has run ahead of the maths

Read any 2025 supervisory speech on systemic or compound risk and you will find the word cascade. The Bank of England has used it of climate physical risk transmitting into financial stability. EIOPA has used it of climate stress transmitting into insurer solvency. The IAIS has used it of operational concentration transmitting into systemic risk. The IFoA's Planetary Solvency programme uses it as the load-bearing concept of the entire workstream.

The technical infrastructure beneath the word is thin. In most cases the cascade is asserted narratively and aggregated quantitatively through a correlation matrix calibrated on data that did not contain a cascade. The result is a profession that talks about cascading risk in the executive summary and prices it as if cascades did not happen.

Defect 1 — Linear propagation

Simple cascading-risk models propagate a shock as a sequence of weighted edges in a directed graph. Damage at the receiving node is approximately the product of the channel weights times the original shock. This structure is intuitive, traceable, and wrong in three specific ways for cross-domain transmission in insurance:

• Convexity at the receiver — a 2× shock typically produces more than 2× damage because the receiver's defences are themselves stress-dependent.
• Path dependence — a shock arriving at a domain via two pathways doesn't produce additive damage. Timing, prior weakening, and mitigation availability all interact.
• Feedback — real cascades are rarely directed acyclic graphs. Linear propagation models cannot represent feedback at all.

Defect 2 — Stationary calibration

Channel coefficients are typically calibrated on historical co-movement during quiescent regimes. Apply that number in stress, and you are implicitly asserting the channel transmits the same way under load as when relaxed. Three sources of non-stationarity bite hard in practice: mitigation depletion (reinsurance consumed, capital drawn, third-parties bottlenecked); behavioural shift (regulators, counterparties, competitors all behave differently under stress); technological obsolescence (cyber concentration, cloud consolidation, parametric trigger architectures aren't in the historical calibration window).

Defect 3 — The missing seventh domain

Most cascading-risk frameworks in production today were designed in the financial-stability tradition: nodes are firms, edges are claims, transmission is balance-sheet. They handle insurance and credit reasonably, operational poorly, climate via bolt-on overlay, and the regulatory channel — the channel by which a single shock generates supervisory action that constrains future capacity — barely at all. The regulatory channel is the most under-modelled of the seven, and arguably the most consequential. A capital cost from a supervisory letter that constrains underwriting capacity by 10% for two years is, in present value, often larger than the immediate insurance loss that triggered it.

The Abgalis Engine alternative

The Abgalis Engine treats transmission channels as first-class entities. Channels are calibrated regime-aware, the seven domains include the regulatory channel as a peer, and the architecture is iterative rather than analytic. What this delivers in operational terms is not a different SCR number — it's a different account of how a given SCR number arose, and which mitigations actually reduce the path that produced it. That's what enables defensible reverse stress, defensible disclosure narrative, and defensible engagement with supervisors who are now asking "trace the shock through your business" as a standing question.