Interpolated Rate Calculator

Interpolated Rate Calculator

Estimated Interpolated Rate

function calculateInterpolatedRate() { var x1 = parseFloat(document.getElementById('lowerTenor').value); var y1 = parseFloat(document.getElementById('lowerRate').value); var x2 = parseFloat(document.getElementById('upperTenor').value); var y2 = parseFloat(document.getElementById('upperRate').value); var x = parseFloat(document.getElementById('targetTenor').value); var resultBox = document.getElementById('interpolationResultBox'); var resultValue = document.getElementById('interpolationValue'); var errorBox = document.getElementById('interpolationError'); errorBox.style.display = 'none'; resultBox.style.display = 'none'; if (isNaN(x1) || isNaN(y1) || isNaN(x2) || isNaN(y2) || isNaN(x)) { errorBox.innerText = "Please fill in all fields with valid numbers."; errorBox.style.display = 'block'; return; } if (x2 === x1) { errorBox.innerText = "Upper tenor and Lower tenor cannot be the same (division by zero)."; errorBox.style.display = 'block'; return; } // Linear Interpolation Formula: y = y1 + (x – x1) * (y2 – y1) / (x2 – x1) var y = y1 + (x – x1) * (y2 – y1) / (x2 – x1); resultValue.innerText = y.toFixed(4) + "%"; resultBox.style.display = 'block'; }

Understanding Interpolated Rates

In finance and mathematics, an interpolated rate is a method used to estimate a specific value that falls between two known data points. This is most commonly used in bond markets and treasury yield curves when you need to find the interest rate for a specific maturity that isn't actively traded or quoted.

The Linear Interpolation Formula

This calculator utilizes the standard linear interpolation formula:

Rate = R1 + (T – T1) × ((R2 – R1) / (T2 – T1))

• T: The target tenor (time period) you want the rate for.
• T1: The shorter known tenor (Lower Tenor).
• T2: The longer known tenor (Upper Tenor).
• R1: The rate associated with the shorter tenor.
• R2: The rate associated with the longer tenor.

Practical Example

Imagine you are looking for the 45-day interest rate, but the market only provides quotes for 30 days and 60 days:

• 30-Day Rate (Lower): 4.00%
• 60-Day Rate (Upper): 5.00%
• Target: 45 Days

Since 45 days is exactly halfway between 30 and 60, the linear interpolation would result in a rate of 4.50%. This calculator automates that process for any set of tenors and rates, whether they are measured in days, months, or years.

When is this used?

Financial analysts and traders use interpolated rates for:

• Yield Curve Construction: Filling in gaps in the sovereign or corporate yield curves.
• Valuing Swaps: Determining the floating or fixed leg rates for non-standard periods.
• Loan Pricing: Setting rates for custom-duration loans that don't match standard bank "buckets" (like a 7-month loan).
• Zero-Coupon Curves: Stripping and interpolating rates to discount future cash flows.

Note: Linear interpolation assumes a straight line between two points. While highly effective for short intervals, it may not account for "bumps" or curvature in volatile market environments.