Interest Rate Parity Calculator

We have prepared this interest rate parity calculator to help you calculate the currency forward price using both the covered and uncovered interest rate parity formulas. These theories assume that future currency exchange rates are affected by the interest rates of the price and base currency. You can use our interest rate calculator and real interest rate calculator to understand more about this topic.

This article will help you understand the covered and uncovered interest rate parity and how to calculate the current forward price using these theories. We will also demonstrate some uncovered and covered interest rate parity examples to help you understand the concepts.

Currency forward is an agreement between two parties that allows one of the parties to buy or sell their currency at hand at a predetermined currency rate in the future. Compared to currency futures, currency forwards allow parties to tailor their terms to fit their specific needs. Furthermore, upfront payment is not required in using currency forwards.

Covered interest rate parity is a theory that estimates the currency forward price based on the no-arbitrage assumption. This means that if the currency forward price in the market is the same as the calculated currency forward price using the covered interest rate parity formula, no one in the market will earn risk-free profits through arbitrage. Please check out our risk calculator to understand more.

Uncovered interest rate parity estimates the currency forward price based on the interest rate differential between the two countries. The theory assumes that the difference between the interest rates of the two countries equals the relative change in the currency exchange rate.

To understand the calculation of the two theories, let's take the currency forward of the USD/EUR as an example. USD stands for the United States dollar, and the EUR stands for the Euro.

• Currency forward: USD/EUR;
• Number of days in the forward contract: 90 days;
• Price currency: USD;
• Base currency: EUR;
• Annualised price currency interest rate: 0.8%; and
• Annualised base currency interest rate: 3.2%.

The calculation using the covered interest rate parity requires 4 steps:

1. Calculate the price currency interest rate

   To calculate the price currency interest rate, we need to adjust the annualized price currency interest rate. USD is the price currency, and the annualized interest rate for USD is 0.8%.

   The formula to calculate price currency is as follows:

   price currency interest rate = annualised price currency interest rate × (days / 360)

   Thus, the price currency interest rate for this currency forward interest rate is 0.8% × (90 / 360) = 0.2%.

2. Calculate the base currency interest rate

   The base currency for this example is EUR, and the annualized interest rate for EUR is 3.2%. Similarly, we can perform the calculation using the formula as follow:

   base currency interest rate = annualised base currency interest rate × (days / 360)

   Hence, the base currency interest rate for this currency forward interest rate is 3.2% × (90 / 360) = 0.8%.

3. Get the current spot price

   We can determine the spot rate by simply googling or obtaining it on Xe.

   The current spot price for USD/EUR is 0.1735.

4. Calculate the currency forward price

   The final step is to calculate the currency forward price using the following covered interest rate parity formula:

   currency forward price = spot price × (1 + price currency interest rate) / (1 + base currency interest rate)

   The price of our USD/EUR currency forward contract is 0.1735 × (1.002 / 1.008) = 0.1725.

We will use the same currency forward as the last example to calculate the currency forward price.

The uncovered interest rate parity calculation requires 4 steps. The first 3 steps are the same as the last example, which are:

1. Calculate the price currency interest rate;

2. Calculate the base currency interest rate; and

3. Determine the current spot price.

The last step is to calculate the currency forward price but with a different formula.

4. Calculate the currency forward price:

   The uncovered interest rate parity formula is shown below where:

   • SP is the spot price; and
   • r is the interest rate.

   Hence, the USD/EUR currency forward contract's price is:

   0.1735 × (1 - (0.2% - 0.8%)) = 0.1725.

The interest rate parity is a no-arbitrage theory. This means that it calculates the price based on the assumption that arbitrage is not possible. The theory also assumes that the market is frictionless. A frictionless market has no external forces, such as transaction costs. These assumptions are unrealistic in real-life applications.

Hence, all in all, interest rate parity will hold when the market is stable and there is a free flow of capital. However, when external forces such as regulations come into play, the interest rate parity might not produce accurate predictions.