CIR Bond Price (Cox-Ingersoll-Ross)
Computes the price of a zero-coupon bond with the Cox-Ingersoll-Ross model, the successor to Vasicek that fixes its biggest flaw: CIR prevents negative interest rates, because the volatility shrinks as the rate approaches zero. It also has mean reversion and yields an affine closed form for the bond price. It's one of the most used short-rate models in practice. Enter the reversion speed, the long-run mean, the volatility, the current rate and the maturity.
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CIR Bond Price (Cox-Ingersoll-Ross)
Computes the price of a zero-coupon bond with the Cox-Ingersoll-Ross model, the successor to Vasicek that fixes its biggest flaw: CIR prevents negative interest rates, because the volatility shrinks as the rate approaches zero. It also has mean reversion and yields an affine closed form for the bond price. It's one of the most used short-rate models in practice. Enter the reversion speed, the long-run mean, the volatility, the current rate and the maturity.
The rate model that won't let the rate go negative
The Vasicek model was revolutionary, but it had an awkward flaw: it allowed interest rates to go negative, something that for decades seemed absurd. Cox, Ingersoll and Ross fixed this in 1985 with a clever change: they made the rate's volatility shrink as it approaches zero, creating a natural floor that keeps it from crossing into negative territory.
Like Vasicek, CIR describes the short rate reverting to a long-run mean, and it also yields an affine closed form for the bond price. The difference is in that square-root-of-the-rate term in the volatility, which changes the whole behavior. It's one of the most used short-rate models, the basis for extensions and for credit-risk models.
Enter the reversion speed, the long-run mean, the rate volatility, the current short rate and the maturity. The tool returns the bond price as a fraction of face and the implied continuous yield. Compare it with Vasicek at the same parameters to see how the positivity restriction changes the result.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.