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.
Nelson-Siegel Yield Curve
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Svensson Yield Curve
Computes the spot rate with the Svensson curve, the extension of the Nelson-Siegel model that adds a second hump to fit more complex yield curves. With six parameters (four betas and two lambdas), it captures shapes Nelson-Siegel can't, which is why it's the choice of central banks like the ECB and the Bundesbank to publish their curves. Enter the four betas in percent, the two lambdas and the desired maturity.
Par Swap Rate
Computes the par swap rate from discount factors: the fixed rate that makes the interest rate swap's value zero at inception, equating the fixed and floating legs. The formula is (1 − last discount factor) divided by the sum of discount factors weighted by the period. It's a swap's market quote and the basis for marking existing positions to market. Enter the list of discount factors by payment date and the year-fraction of each period.
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.