Smith-Wilson extrapolation
Interpolation and extrapolation method building the regulatory risk-free curve, fitting observed liquid points exactly and converging to the ultimate forward rate beyond.
A life insurer discounts cash flows at fifty years while the market quotes liquidly only out to twenty. An extrapolation convention is therefore needed, and Solvency II adopted the Smith-Wilson method. It builds a curve passing exactly through the observed points up to the last liquid point, then converging to the ultimate forward rate at a speed governed by a single parameter, calibrated so that convergence is reached at a given maturity. Its properties explain its adoption: one family of functions, one free parameter, an exact fit to market data, and a result every participant can reproduce from published inputs. The criticism, constant since 2016, is that beyond the last liquid point the curve holds no market information at all: it is driven entirely by the ultimate forward rate, even where trades exist at thirty or forty years. The Solvency II review, adopted on November 27, 2024 and published in January 2025 (Directive (EU) 2025/2), corrects precisely that by bringing market information in beyond the last liquid point, which moves the regulatory curve closer to the observable one.
Under the Solvency II regime applied since January 1, 2016, the euro's last liquid point is set at twenty years, and convergence to the ultimate forward rate is reached at sixty. On an annuity liability with a duration above fifteen years, most of the present value is computed on the extrapolated part of the curve. The extrapolation convention then weighs more on prudential own funds than the level of rates actually quoted. Directive (EU) 2025/2 replaces, from January 30, 2027, the last liquid point with a first smoothing point, also at twenty years for the euro. It also revises the convergence, with a phased implementation through 2032.
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