Forward Forward Rate Calculator
.calculator-container {
font-family: sans-serif;
border: 1px solid #ddd;
padding: 20px;
border-radius: 8px;
max-width: 500px;
margin: 20px auto;
background-color: #f9f9f9;
}
.calculator-title {
text-align: center;
color: #333;
margin-bottom: 20px;
}
.calculator-inputs {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 15px;
margin-bottom: 20px;
}
.input-group {
display: flex;
flex-direction: column;
}
.input-group label {
margin-bottom: 5px;
font-weight: bold;
color: #555;
}
.input-group input {
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
}
button {
grid-column: 1 / -1;
padding: 12px 20px;
background-color: #007bff;
color: white;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 16px;
transition: background-color 0.3s ease;
}
button:hover {
background-color: #0056b3;
}
.calculator-result {
border-top: 1px solid #eee;
padding-top: 15px;
margin-top: 15px;
background-color: #fff;
padding: 15px;
border-radius: 4px;
}
.calculator-result h3 {
color: #333;
margin-bottom: 10px;
}
.calculator-result p {
color: #007bff;
font-size: 1.1em;
font-weight: bold;
text-align: center;
}
function calculateForwardRate() {
var spotRate1 = parseFloat(document.getElementById("spotRate1").value);
var period1 = parseFloat(document.getElementById("period1").value);
var spotRate2 = parseFloat(document.getElementById("spotRate2").value);
var period2 = parseFloat(document.getElementById("period2").value);
var resultElement = document.getElementById("forwardRateResult");
if (isNaN(spotRate1) || isNaN(period1) || isNaN(spotRate2) || isNaN(period2)) {
resultElement.textContent = "Please enter valid numbers for all fields.";
return;
}
if (period1 <= 0 || period2 <= 0 || period2 <= period1) {
resultElement.textContent = "Periods must be positive and period 2 must be greater than period 1.";
return;
}
// Ensure rates are in decimal form for calculation (e.g., 5% becomes 0.05)
var rate1 = spotRate1;
var rate2 = spotRate2;
// Formula for forward rate: F(t1, t2) = [(1 + S2*t2) / (1 + S1*t1)]^(1/(t2-t1)) – 1
// Using simple interest for compounding here for common interpretation of spot rates in basic context.
// For continuous compounding, it would be exp(S2*t2) / exp(S1*t1) ^ (1/(t2-t1)) – 1
var numerator = 1 + rate2 * period2;
var denominator = 1 + rate1 * period1;
if (denominator <= 0) {
resultElement.textContent = "Calculation error: Denominator is zero or negative.";
return;
}
var exponent = 1 / (period2 – period1);
var forwardRate = Math.pow(numerator / denominator, exponent) – 1;
if (isNaN(forwardRate) || !isFinite(forwardRate)) {
resultElement.textContent = "Calculation error. Please check your inputs.";
} else {
resultElement.textContent = (forwardRate * 100).toFixed(4) + "%";
}
}
Understanding Forward Forward Rates
A forward rate represents the interest rate agreed upon today for a financial transaction that will take place at some point in the future. The "forward forward rate" specifically refers to an interest rate that applies to a period starting at a future date (t1) and ending at a later future date (t2). It's essentially a rate for a future loan or investment that begins after a current period has ended.
The calculation is derived from the relationship between spot rates and forward rates. A spot rate (S) for a period (t) is the interest rate for a loan or investment from today (time 0) until time t. The forward forward rate (F) between time t1 and t2 can be calculated using the spot rates for periods t1 and t2.
The formula used in this calculator, assuming simple interest for simplicity in illustrating the concept with spot rates, is:
Forward Rate = [(1 + Spot Rate 2 * Period 2) / (1 + Spot Rate 1 * Period 1)] ^ (1 / (Period 2 - Period 1)) - 1
Where:
Spot Rate 1: The annual interest rate for the first period (from time 0 to t1).Period 1: The length of the first period in years (t1).Spot Rate 2: The annual interest rate for the second, longer period (from time 0 to t2).Period 2: The length of the second period in years (t2).Period 2 - Period 1: The duration of the forward period.
This calculation effectively isolates the implied interest rate for the period between t1 and t2, based on the prevailing spot rates for the shorter and longer maturities. This concept is crucial in fixed-income markets for pricing bonds, managing interest rate risk, and understanding market expectations about future interest rates.
Example:
Let's say:
- The 1-year spot rate (Spot Rate 1) is 5% (0.05). So, Period 1 = 1 year.
- The 3-year spot rate (Spot Rate 2) is 6% (0.06). So, Period 2 = 3 years.
We want to find the implied interest rate for the period between year 1 and year 3 (a 2-year period).
Using the formula:
Forward Rate = [(1 + 0.06 * 3) / (1 + 0.05 * 1)] ^ (1 / (3 - 1)) - 1
Forward Rate = [(1 + 0.18) / (1 + 0.05)] ^ (1 / 2) - 1
Forward Rate = [1.18 / 1.05] ^ 0.5 - 1
Forward Rate = [1.1238] ^ 0.5 - 1
Forward Rate = 1.0601 - 1
Forward Rate = 0.0601
So, the forward forward rate for the period starting in 1 year and ending in 3 years is approximately 6.01%. This means the market expects an annualized rate of 6.01% to prevail over the second and third years.