Vasicek Bond Price
Computes the price of a zero-coupon bond with the Vasicek model, the first short-rate interest-rate model with mean reversion. It describes the short rate oscillating around a long-run mean and yields a closed form for the bond price from four parameters: reversion speed, mean, volatility and current rate. Despite allowing negative rates, it's the foundation of the whole family of term-structure models. Enter the parameters and the maturity, and see the price and implied yield.
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Vasicek Bond Price
Computes the price of a zero-coupon bond with the Vasicek model, the first short-rate interest-rate model with mean reversion. It describes the short rate oscillating around a long-run mean and yields a closed form for the bond price from four parameters: reversion speed, mean, volatility and current rate. Despite allowing negative rates, it's the foundation of the whole family of term-structure models. Enter the parameters and the maturity, and see the price and implied yield.
Modeling the rate that always comes home
Interest rates have a known stubbornness: they rise, they fall, but they tend to return to a long-run equilibrium level. In 1977, Oldřich Vašíček captured this mean reversion in the first short-rate model, and out of it came a closed form for the price of a zero-coupon bond. It was the starting point of all modern term-structure theory.
The model describes the short rate with three forces: the speed at which it's pulled back, the level it converges to and the intensity of the random shocks. From these, the bond price comes out as an elegant exponential function. Its famous limitation is allowing negative rates, which motivated successors like the CIR, which prevents it, and Hull-White, which fits the observed curve.
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 value and the implied continuous yield. It's the tool for understanding how a short-rate model's parameters translate into prices and curves.
Related Tools
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.
Bond Dirty Price
Computes the dirty price of a bond: the clean price plus the interest accrued since the last coupon. The clean price is what shows up in quotes, but what actually changes hands at settlement is the dirty price, because the buyer has to reimburse the seller for the interest already run up. The tool works out the accrued interest on a linear basis and adds it to the clean price, returning both parts. Enter the clean price, the face value, the annual coupon rate, the coupon frequency, the days since the last coupon and the days in the period.
Bond Price from YTM
Computes the price of a coupon bond from its yield to maturity, discounting all future coupons and the face value to present: P = C·[1 − (1+i)^(−n)]/i + F·(1+i)^(−n). It's the inverse of computing the YTM and the foundation of fixed-income pricing. When the coupon exceeds the YTM, the bond trades at a premium; when below, at a discount. The calculation divides coupon and yield by the payment frequency. Enter the face value, the coupon rate, the YTM, the years and the coupons per year.
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.