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Market risk benefits | 6 Months Ended
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Jun. 30, 2023
Market Risk Benefit [Abstract] |
Market risk benefits | Market risk benefits Our reinsurance programs covering variable annuity guarantees, comprising guaranteed living benefits (GLB) and guaranteed minimum death benefits (GMDB), meet the definition of Market risk benefits (MRB). The following table presents a roll-forward of MRB:
| Six Months Ended June 30
(in millions of U.S. dollars) | 2023 |  | 2022
Balance – beginning of period | $ | 800 |  |  | $ | 812 |
Balance, beginning of period, before effect of changes in the instrument-specific credit risk | 776 |  |  | 755 |
Interest rate changes | 37 |  |  | (356) |
Effect of changes in equity markets | (144) |  |  | 482 |
Effect of changes in volatilities | 31 |  |  | 62 |
Effect of timing and all other | 6 |  |  | (46) |
Balance, end of period, before effect of changes in the instrument-specific credit risk | $ | 706 |  |  | $ | 897 |
Effect of changes in the instrument-specific credit risk | 16 |  |  | 17 |
Balance – end of period | $ | 722 |  |  | $ | 914 |
Weighted-average age of policyholders (years) | 73 |  | 73
Net amount at risk | $ | 2,048 |  |  | $ | 2,667 |
Excluded from the table above are MRB gains (losses) of $(192) million and $158 million for the six months ended June 30, 2023 and 2022, respectively, reported in the Consolidated statements of operations, relating to the market risk benefits' economic hedge and other net cash flows. There is no reinsurance recoverable associated with our liability for MRB. For MRB reinsurance, Chubb estimates fair value using an internal valuation model which includes a number of factors including interest rates, equity markets, credit risk, current account value, market volatility, expected annuitization rates and other policyholder behavior, and changes in policyholder mortality. All reinsurance treaties contain claim limits, which are also factored into the valuation model.
|  |  | Valuation Technique |  | Significant Unobservable Inputs |  | June 30, 2023 |  | June 30, 2022
|  |  | Ranges |  | Weighted Average(1) |  | Ranges |  | Weighted Average(1)
MRB (1) |  |  | Actuarial model |  | Lapse rate |  | 1% – 30% |  | 4.0 | % |  | 3% – 31% |  | 4.0 | %
|  |  |  |  | Annuitization rate |  | 0% – 100% |  | 4.2 | % |  | 0% – 100% |  | 4.4 | %
(1)The weighted-average lapse and annuitization rates are determined by weighting each treaty's rates by the MRB contract's fair value. The most significant policyholder behavior assumptions include lapse rates for MRBs, and GLB annuitization rates. Assumptions regarding lapse rates and GLB annuitization rates differ by treaty, but the underlying methodologies to determine rates applied to each treaty are comparable. A lapse rate is the percentage of in-force policies surrendered in a given calendar year. All else equal, as lapse rates increase, ultimate claim payments will decrease. In general, the base lapse function assumes low lapse rates during the surrender charge period, followed by a "spike" lapse rate in the year immediately following the surrender charge period, and then reverting to an ultimate lapse rate, typically over a 2-year period. This base rate is adjusted downward for policies with more valuable guarantees (policies with guaranteed values far in excess of their account values). Partial withdrawals and the impact of older policyholders with tax-qualified contracts (due to required minimum distributions) are also reflected in our modeling. The GLB annuitization rate is the percentage of policies for which the policyholder will elect to annuitize using the guaranteed benefit provided under the GLB. All else equal, as GLB annuitization rates increase, ultimate claim payments will increase, subject to treaty claim limits. All GLB reinsurance treaties include claim limits to protect Chubb in the event that actual annuitization behavior is significantly higher than expected. In general, Chubb assumes that GLB annuitization rates will be higher for policies with more valuable guarantees (policies with guaranteed values far in excess of their account values). Chubb also assumes that GLB annuitization rates increase as policyholders get older. In addition, it is also assumed that GLB annuitization rates are higher in the first year immediately following the waiting period (the first year the policies are eligible to annuitize using the GLB) in comparison to all subsequent years. Chubb does not yet have fully credible annuitization experience for all clients.The effect of changes in key market factors on assumed lapse and annuitization rates reflect emerging trends using data available from cedants. For treaties with limited experience, rates are established by blending the experience with data received from other ceding companies. The model and related assumptions are regularly re-evaluated by management and enhanced, as appropriate, based upon additional experience obtained related to policyholder behavior and availability of updated information such as market conditions, market participant assumptions, and demographics of in-force annuities.

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