No-arbitrage one-factor term structure models in zero- or negative-lower-bound environments

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One-factor no-arbitrage term structure models where the instantaneous interest rate follows either the process proposed by Vasicek (1977) or by Cox, Ingersoll, and Ross (1985), commonly known as CIR, are parsimonious and analytically tractable. Models based on the original CIR process have the important characteristic of allowing for a time-varying conditional interest rate volatility but are undefined in negative interest rate environments. A Shifted-CIR no-arbitrage term structure model, where the instantaneous interest rate is given by the sum of a constant lower bound and a non-negative CIR-like process, allows for negative yields and benefits from similar tractability of the original CIR model. Based on the U.S. and German yield curve data, the Vasicek and Shifted-CIR specifications, both considering constant and time-varying risk premia, are compared in terms of information criteria and forecasting ability. Information criteria prefer the Shifted-CIR specification to models based on the Vasicek process. It also provides similar or better in-sample and out-of-sample forecasting ability of future yield curve movements. Introducing a time variation of the interest rate risk premium in no-arbitrage one-factor term structure models is instead not recommended, as it provides worse information criteria and forecasting performance.

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    • Figure 1. In-sample and out-of-sample 6-month-ahead yield variation forecasting ability in comparison to the random walk hypothesis
    • Figure 2: In-sample and out-of-sample short-term rate volatility forecasting
    • Figure 3. Out-of-sample parameter estimates for the Vasicek models
    • Figure 4. Out-of-sample parameter estimates for the S-CIR models with non-positive lower bound
    • Figure 5. Out-of-sample parameter estimates for the S-CIR models with an unconstrained lower bound
    • Figure 6. Out-of-sample 6-month-ahead yield variation forecasting ability in comparison to the random walk hypothesis (sub-samples pre-2008 and post-2008)
    • Table 1. In-sample parameter estimates
    • Table 2. Data and model-implied averages and volatilities of bond yields
    • Conceptualization
      Andrea Tarelli
    • Data curation
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      Andrea Tarelli
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