focalinterest.net

Tag: Actuarial Science & Risk Modeling

  • Unweighted HJM framework allows negative yield modeling

    What the study found

    The study proposes an unweighted function-space version of the Heath–Jarrow–Morton (HJM) framework for modeling the full yield curve, which is the set of interest rates across different maturities. The authors report that this setup can be calibrated to real-world yield data and can allow for negative interest rates.

    Why the authors say this matters

    The authors say the new setting avoids a drawback of earlier HJM implementations, where the choice of exponential weight cannot be estimated from market data and has no objective interpretation. They suggest the framework is useful for prediction and uncertainty quantification, and that it can handle the negative Euro bond yields observed in their sample.

    What the researchers tested

    The researchers discretized the HJM equation using a finite difference method and built a semiparametric model. They calibrated it on real-world yield data using a new functional principal component analysis-based approach, and they backtested and benchmarked it against a one-factor Vasicek model using historical data.

    What worked and what didn't

    The abstract says the proposed framework was calibrated on real-world yield data and used to illustrate simulation capabilities for prediction and uncertainty quantification. It also notes that, unlike widely studied U.S. treasuries, negative interest rates were observed for AAA Euro Bonds in the sample period, and the framework allows for negative yields.

    What to keep in mind

    The abstract does not provide detailed numerical results, performance metrics, or a full account of the backtesting outcomes. It also does not describe limitations beyond noting that earlier weighted function-space choices could not be estimated from market data.

    • The paper introduces an unweighted function-space setting for the Heath–Jarrow–Morton framework.
    • The authors say earlier exponentially weighted settings have weights that cannot be estimated from market data.
    • The model was discretized with a finite difference approach and calibrated with a functional principal component analysis-based method.
    • Backtesting and benchmarking were done against a one-factor Vasicek model.
    • The sample included AAA Euro Bonds with negative interest rates, and the framework allows negative yields.

  • Expectiles minimize basis risk in parametric insurance payments

    What the study found

    The study found that basis risk-minimizing payment schemes for pure parametric and parametric index insurance contracts can be written as conditional expectiles of policyholders’ true loss, given a compensation-triggering incident. Expectiles are asymmetric averages that weight losses and gains differently.

    Why the authors say this matters

    The authors say this is relevant because parametric insurance is operationally efficient and cost effective, but it can create basis risk, meaning payouts may differ from actual damage. The study suggests a framework for reducing that mismatch while keeping the parametric structure.

    What the researchers tested

    The researchers worked in an asymmetrically weighted mean square error framework. They analyzed pure parametric and parametric index insurance contracts, connected the results to stochastic orderings, and used regression approaches to show how the ideas could be implemented in practice.

    What worked and what didn't

    The study reports that conditional expectiles characterize the basis risk-minimizing payment schemes in the setting they consider. It also says regression approaches allow easy implementation in practice. The results were visualized for parametric coverage in cyber risks and agricultural insurance.

    What to keep in mind

    The abstract does not describe empirical testing beyond the visualized examples in cyber risks and agricultural insurance. It also does not state limitations beyond the scope of the contracts and framework analyzed.

    • Basis risk in parametric insurance is the gap between payouts and actual damage.
    • The study links basis risk-minimizing payments to conditional expectiles.
    • The framework covers pure parametric and parametric index insurance contracts.
    • Regression approaches are presented as a practical way to implement the results.
    • Examples are visualized for cyber risks and agricultural insurance.

  • GMIB valuation yields an analytic solution with faster computation

    What the study found

    The study found that a numéraire transformation approach can be used to value guaranteed minimum income benefits (GMIBs), a guarantee in variable annuities. It also found an analytic solution under two different Benefit Base function settings, and reported much lower computation time than standard Monte Carlo simulation.

    Why the authors say this matters

    The authors suggest the method is useful because GMIBs are part of variable annuities, which they describe as retirement products with innovative guarantee features. The findings indicate the proposed approach may improve computational accuracy and efficiency for GMIB valuation.

    What the researchers tested

    The researchers built a modelling framework for GMIB valuation that includes three sources of uncertainty: interest risk, mortality risk, and investment risk. They modeled these risks stochastically, allowed for interdependence between interest and mortality risks, and used numéraire transformation with forward and endowment-risk-adjusted measures.

    What worked and what didn't

    For two distinct Benefit Base function settings, the approach produced an analytic solution for GMIB. In numerical tests, the proposed method outperformed standard Monte Carlo simulation as a benchmark, with an average reduction of 99% in computing time; the abstract does not report any specific failures or cases where the method performed worse.

    What to keep in mind

    The abstract does not provide details on the dataset, calibration, or the exact numerical settings used in the experiments. It also does not describe limitations beyond noting the two Benefit Base function settings and the sensitivity analysis.

    • The study values guaranteed minimum income benefits in variable annuities.
    • It models interest risk, mortality risk, and investment risk together.
    • The approach accounts for interdependence between interest and mortality risks.
    • An analytic solution was derived for two Benefit Base function settings.
    • The method reduced computing time by an average of 99% versus Monte Carlo simulation.