Smith-Wilson Extrapolation
A curve-fitting method, used mainly by insurance regulators, that blends observed long-dated rates smoothly toward a single assumed "ultimate forward rate" far out the curve where no liquid market exists.
Beyond about 20-30 years, government and swap markets often have too few trades to produce a reliable rate — there simply isn't enough liquidity to trust the quotes. Insurance regulators still need a discount curve out to 50 or 100 years to value long-dated liabilities like annuities, so they need a rule for extending the curve past where real prices exist.
Smith-Wilson extrapolation is that rule. It takes the last liquid, trustworthy point on the curve and smoothly bends the forward rate toward a fixed long-run assumption called the ultimate forward rate (UFR) — a regulator-set number, often around 3.3-4.2% depending on jurisdiction and year, meant to reflect long-run expected inflation and real growth rather than any observed price.
Smith-Wilson extrapolation doesn't estimate long-dated rates from data that doesn't exist — it smoothly blends the last reliable market point into a fixed, regulator-chosen long-run rate, guaranteeing the curve looks sensible everywhere valuations need it.
How the blend works
The method uses a mathematical smoothing function (a specific kernel) so that near the last liquid point the curve matches observed rates closely, and as maturity increases the influence of the kernel fades, letting the forward rate converge on the UFR by a chosen convergence maturity, often 40-60 years out.
This matters mainly for solvency reporting: because the UFR is a policy assumption, not a market observation, small changes to it (which regulators do make periodically) can shift the reported value of decades' worth of insurance liabilities without any change in market rates at all.
Related concepts
Practice in interviews
Further reading
- EIOPA, 'Technical Documentation of the Risk-Free Interest Rate Term Structure'