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The FHFA methodology to construct a historically-based shock for a given interest rate is to measure the absolute change at each term point on the corresponding yield curve over a six-month horizon, and then impose that absolute change on the current measure of that yield curve. However, because the current rate environment may differ significantly from the historical rate environment, imposing the historical shock on the current rate can result in a shock scenario that is implausible. Implausible shock scenarios include any that contain negative values for interest rates, and those where the resulting spread between any two different interest rates is inconsistent with the historically observed spread. To ensure that the resulting shock scenarios are plausible, FHFA uses a technique known as parsimonious factorization to represent each yield curve as a five-factor equation, and then applies measures of the shock made in parameter space to the current yield curve parameters to determine the shocked yield curve. This approach facilitates a straightforward means to impose constraints on generating the shock scenario that ensure its plausibility.
The FHFA scenarios contain interest rate shocks to each of the Treasury, Libor-Swap, and the Federal Home Loan Bank System Cost of Funds yield curves. Banks that must involve other, or miscellaneous, interest rates to estimate portfolio value may determine shocked values for those rates by applying a constant measure of the current yield curve spread between the miscellaneous rate and any one of the three rates FHFA provides. The shocked miscellaneous yield curve is then derived by applying the constant measure of spread to the shocked version of the selected FHFA provided yield curve.
The FHFA scenarios also contain shocks to two measures of implied volatility and to the agency option-adjusted-spread (OAS). Implied volatility shocks are presented for at-the-money swaptions, and in- and out-of-the-money caps. Using parsimonious factorization, the parameters that define each implied volatility surface are estimated and then related to the interest rate parameters. Applying the historical shocks to the interest rate parameters is then translated into corresponding shocks to the volatility parameters. Agency OAS shocks are derived by first estimating the relationship between changes in OAS and changes in interest rates, where the latter are measured in parameter space. Applying the historical shocks to the interest rate parameters is once again translated into shocks applicable to the agency OAS.
For a more detailed description of the methodology, see the working papers listed below. Questions or comments can be sent to
All scenarios posted prior to 2020 are intended for
testing purposes only.
Please note that only the quarter-end monthly scenarios are applicable for reporting risk-based-capital requirements. The off-quarter-end monthly scenarios are being provided at this time for testing and monitoring purposes, and may not be subject to the same degree of validation as the quarter-end scenarios.
Shocked yield curves for Treasury, Libor-Swap, and FHLBank COF—also includes shock size
[All XLSX Files]
Additive shocks to implied volatility for at-the-money swaptions and in- and out- of-the-money caps
Additive shocks to OAS for agency securities
PolyPaths ready version of all shock data
[XLSX and CSV Files]
A number of key assumptions and application directions are required in constructing the market risk scenarios and applying the shocks to the portfolio. They are described on the
Assumptions and Directions Page, which will be updated as appropriate.
Last Update of the
Assumptions Details and Application Directions Page: 5/29/2018
WP 13-2: Generating Historically-Based Stress Scenarios Using Parsimonious Factorization
WP 15-3: Additional Market Risk Shocks: Prepayment Uncertainty and Option-Adjusted Spreads
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