Interest Rate Parity Calculator

What is Interest Rate Parity (IRP)?

Interest Rate Parity (IRP) is a fundamental concept in foreign exchange finance that establishes a relationship between spot exchange rates, forward exchange rates, and nominal interest rates of two countries. According to IRP theory, the interest rate differential between two nations equals the differential between the forward exchange rate and the spot exchange rate.

Covered Interest Rate Parity Formula

Under Covered Interest Rate Parity (CIRP), forward contracts are used to eliminate foreign exchange rate risk. The theoretical forward exchange rate formula is:

$$F = S \times \frac{1 + i_d \times t}{1 + i_f \times t}$$

Where:

• F: Theoretical Forward Exchange Rate.
• S: Current Spot Exchange Rate.
• i_d: Domestic Nominal Interest Rate (annualized).
• i_f: Foreign Nominal Interest Rate (annualized).
• t: Time to maturity in years (e.g., 6 months = 0.5 years).

Forward Premium and Arbitrage

When the domestic interest rate is higher than the foreign interest rate ($i_d > i_f$), the foreign currency trades at a forward premium ($F > S$). Conversely, when foreign interest rates exceed domestic interest rates, the foreign currency trades at a forward discount ($F < S$).

If the market forward rate differs significantly from the theoretical forward rate calculated by IRP, arbitrageurs can exploit covered interest arbitrage opportunities until market prices realign with parity.

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