.libor-calc-container {
padding: 25px;
background-color: #f8f9fa;
border: 1px solid #dee2e6;
border-radius: 8px;
max-width: 600px;
margin: 20px auto;
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
color: #333;
}
.libor-calc-container h2 {
margin-top: 0;
color: #0056b3;
text-align: center;
}
.libor-input-group {
margin-bottom: 15px;
}
.libor-input-group label {
display: block;
font-weight: 600;
margin-bottom: 5px;
}
.libor-input-group input {
width: 100%;
padding: 10px;
border: 1px solid #ced4da;
border-radius: 4px;
box-sizing: border-box;
}
.libor-calc-btn {
width: 100%;
padding: 12px;
background-color: #0056b3;
color: white;
border: none;
border-radius: 4px;
font-size: 16px;
font-weight: bold;
cursor: pointer;
transition: background-color 0.2s;
}
.libor-calc-btn:hover {
background-color: #004494;
}
#libor-result-area {
margin-top: 20px;
padding: 15px;
background-color: #e9ecef;
border-radius: 4px;
display: none;
}
.result-value {
font-size: 24px;
color: #28a745;
font-weight: bold;
text-align: center;
}
.libor-article {
max-width: 800px;
margin: 40px auto;
line-height: 1.6;
color: #444;
}
.libor-article h3 {
color: #222;
border-left: 4px solid #0056b3;
padding-left: 10px;
}
.formula-box {
background: #fff;
border: 1px dashed #0056b3;
padding: 15px;
font-family: "Courier New", Courier, monospace;
margin: 15px 0;
}
Understanding Interpolated LIBOR Rates
In the world of international finance, LIBOR (London Interbank Offered Rate) is typically quoted for standard periods, or "tenors," such as 1 month, 3 months, or 6 months. However, many financial contracts, such as interest rate swaps or bridge loans, may have "broken dates"—durations that do not perfectly match these standard quoted tenors.
Interpolation is the mathematical method used to estimate the interest rate for these specific durations by looking at the rates of the two closest standard tenors. This ensures that the valuation of a financial instrument is accurate and reflects the current yield curve.
The Linear Interpolation Formula
The calculator uses linear interpolation, which assumes a straight-line relationship between the two nearest data points. The formula is expressed as:
Rate = R1 + [ (T – T1) × (R2 – R1) / (T2 – T1) ]
Where:
- R1: Interest rate for the shorter standard tenor.
- R2: Interest rate for the longer standard tenor.
- T: Number of days for the target "broken date" period.
- T1: Number of days in the shorter standard tenor.
- T2: Number of days in the longer standard tenor.
A Practical Example
Imagine you have a loan that matures in 45 days. You look up the current market rates and find:
- 30-day (1 Month) LIBOR is 5.10%
- 60-day (2 Month) LIBOR is 5.40%
To find the 45-day rate, you calculate the difference between the rates (0.30%) and the difference between the days (30 days). The 45-day mark is exactly halfway between 30 and 60 days, so the interpolated rate would be 5.25%.
Why Accuracy Matters
In institutional finance, even a difference of a single "basis point" (0.01%) can result in thousands of dollars in valuation differences on large principal amounts. While LIBOR is being phased out in favor of SOFR (Secured Overnight Financing Rate), the methodology for linear interpolation remains the industry standard for determining "broken date" rates across all benchmark indices.
function calculateLiborInterpolation() {
var targetT = parseFloat(document.getElementById("targetTenor").value);
var t1 = parseFloat(document.getElementById("shortTenor").value);
var r1 = parseFloat(document.getElementById("shortRate").value);
var t2 = parseFloat(document.getElementById("longTenor").value);
var r2 = parseFloat(document.getElementById("longRate").value);
var resultDisplay = document.getElementById("liborResultDisplay");
var resultArea = document.getElementById("liborResultArea");
var noteArea = document.getElementById("liborNote");
if (isNaN(targetT) || isNaN(t1) || isNaN(r1) || isNaN(t2) || isNaN(r2)) {
alert("Please enter valid numerical values for all fields.");
return;
}
if (t2 <= t1) {
alert("Longer tenor must be greater than shorter tenor.");
return;
}
if (targetT t2) {
noteArea.innerHTML = "Note: Your target maturity is outside the provided range. This is technically extrapolation.";
} else {
noteArea.innerHTML = "";
}
// Linear Interpolation Calculation
// Rate = R1 + (T – T1) * (R2 – R1) / (T2 – T1)
var calculatedRate = r1 + ((targetT – t1) * (r2 – r1) / (t2 – t1));
document.getElementById("libor-result-area").style.display = "block";
resultDisplay.innerHTML = calculatedRate.toFixed(4) + "%";
}