Enter annualized spot rates for each consecutive period, separated by commas. Example: For a 3-year semi-annual bond, enter 6 rates (0.5y, 1y, 1.5y, 2y, 2.5y, 3y).
Calculated Bond Price:–
Periods to Maturity:–
Total Coupon Cash Flow:–
Present Value of Principal:–
Understanding Bond Pricing with Spot Rates
Valuing a bond using a single Yield to Maturity (YTM) assumes that the yield curve is flat—meaning the interest rate is the same for all maturities. However, in real financial markets, the term structure of interest rates is rarely flat. Interest rates for short-term loans usually differ from long-term loans.
To calculate the true "arbitrage-free" price of a bond, one must discount each specific cash flow (coupon payment or principal repayment) by the specific spot rate corresponding to the timing of that cash flow. This calculator allows you to input a series of spot rates to determine the precise value of a bond.
How the Calculation Works
The price of the bond is the sum of the present values of all future cash flows. The formula used is:
Price = Σ [ C / (1 + zt/n)t ] + [ F / (1 + zN/n)N ]
Where:
C: Coupon payment per period (Face Value × Annual Coupon Rate ÷ Frequency)
F: Face Value (Principal)
zt: Annualized zero-coupon spot rate for period t
n: Compounding frequency per year
t: Period number (1, 2, …, N)
Why Use Spot Rates Instead of YTM?
Using spot rates prevents arbitrage opportunities. If a bond were priced using a single average rate (YTM) that differed from the aggregate of the individual spot rates, traders could strip the bond (separate coupons from principal) and sell the parts for a risk-free profit.
Example Calculation
Consider a 2-year bond with a face value of $1,000 and a 5% annual coupon paid annually.
Year
Cash Flow
Spot Rate (%)
Discount Factor
Present Value
1
$50
3.0%
1 / (1.03)¹ = 0.9709
$48.54
2
$1,050
4.0%
1 / (1.04)² = 0.9246
$970.83
Total
$1,019.37
In this example, the bond price is the sum of the present values: $48.54 + $970.83 = $1,019.37.
Key Terms Defined
Spot Rate: The yield to maturity on a zero-coupon bond for a specific maturity. It represents the interest rate for a single cash flow at a specific future date.
Term Structure: Also known as the yield curve, this is the relationship between interest rates and different terms to maturity.
Bootstrapping: A method used to construct a spot rate curve from the prices of coupon-bearing bonds.
function calculateBondPrice() {
// Clear previous errors and results
var errorDiv = document.getElementById('bpError');
var resultDiv = document.getElementById('bpResult');
errorDiv.style.display = 'none';
errorDiv.innerHTML = ";
resultDiv.style.display = 'none';
// Get Input Values
var faceValue = parseFloat(document.getElementById('bpFaceValue').value);
var couponRate = parseFloat(document.getElementById('bpCouponRate').value);
var frequency = parseInt(document.getElementById('bpFrequency').value);
var spotRatesString = document.getElementById('bpSpotRates').value;
// Validation Logic
if (isNaN(faceValue) || faceValue <= 0) {
showError("Please enter a valid positive Face Value.");
return;
}
if (isNaN(couponRate) || couponRate < 0) {
showError("Please enter a valid Annual Coupon Rate.");
return;
}
if (!spotRatesString || spotRatesString.trim() === "") {
showError("Please enter at least one Spot Rate.");
return;
}
// Parse Spot Rates
var spotRates = [];
var rawRates = spotRatesString.split(',');
for (var i = 0; i < rawRates.length; i++) {
var val = parseFloat(rawRates[i].trim());
if (!isNaN(val)) {
spotRates.push(val);
}
}
if (spotRates.length === 0) {
showError("Invalid format for Spot Rates. Please use comma-separated numbers (e.g., 2.5, 3.0).");
return;
}
// Calculation Logic
var bondPrice = 0;
var couponPayment = (faceValue * (couponRate / 100)) / frequency;
var totalCouponFlow = 0;
var pvPrincipal = 0;
// Loop through each period (defined by the number of spot rates provided)
for (var t = 0; t < spotRates.length; t++) {
var periodNumber = t + 1;
var currentSpotRate = spotRates[t]; // This is an annualized rate in percent
// Adjust rate for frequency: r / frequency / 100
var periodRate = (currentSpotRate / 100) / frequency;
// Discount Factor: 1 / (1 + r)^t
var discountFactor = 1 / Math.pow((1 + periodRate), periodNumber);
// Determine Cash Flow for this period
var cashFlow = couponPayment;
// If it's the last period, add the Principal (Face Value)
var isMaturity = (t === spotRates.length – 1);
if (isMaturity) {
cashFlow += faceValue;
// Calculate PV of Principal separately for display
pvPrincipal = faceValue * discountFactor;
}
// Add PV of this period's cash flow to total bond price
bondPrice += cashFlow * discountFactor;
totalCouponFlow += couponPayment;
}
// Formatting Results
var formatter = new Intl.NumberFormat('en-US', {
style: 'currency',
currency: 'USD',
minimumFractionDigits: 2,
maximumFractionDigits: 2
});
document.getElementById('resPrice').innerHTML = formatter.format(bondPrice);
document.getElementById('resPeriods').innerHTML = spotRates.length;
document.getElementById('resTotalCoupons').innerHTML = formatter.format(totalCouponFlow);
document.getElementById('resPvPrincipal').innerHTML = formatter.format(pvPrincipal);
resultDiv.style.display = 'block';
}
function showError(message) {
var errorDiv = document.getElementById('bpError');
errorDiv.innerHTML = message;
errorDiv.style.display = 'block';
}