Introduction

This Chapter explores the interest rate parity theorem, an essential concept in the foreign exchange markets. The interest rate parity theorem establishes a relationship between interest rates, exchange rates, and forward exchange rates. By assuming a world without arbitrage opportunities, this theorem plays a crucial role in understanding and calculating forward foreign exchange rates. In this chapter, we will delve into the non-arbitrage assumption, the derivation of the interest rate parity equation, and how it is utilized to estimate forward exchange rates.

Non-Arbitrage Assumption in Foreign Exchange Markets

The interest rate parity theorem is based on the assumption that there are no arbitrage opportunities available in the foreign exchange markets. This means that it is not possible for market participants to exploit interest rate differentials between two currencies to make risk-free profits. If such opportunities were available, traders could borrow in one currency, convert it to another, invest at a higher interest rate, and then convert back at a favorable rate, resulting in riskless gains. The non-arbitrage assumption ensures that market forces quickly eliminate any discrepancies in exchange rates and interest rates.

Calculating Forward Foreign Exchange Rates using Interest Rate Parity

The interest rate parity theorem can be expressed mathematically as follows:

$$F = S \times \left(1+\dfrac{r_{domestic}}{100} \right)^{\dfrac{T}{365}} \times \left(1+\dfrac{r_{foreign}}{100} \right)^{-\dfrac{T}{365}} $$

Where:

• $F$ is the forward exchange rate between the domestic and foreign currencies
• $S$ is the current spot exchange rate between the domestic and foreign currencies
• $r_{domestic}$ is the domestic interest rate
• $r_{foreign}$ ​is the foreign interest rate
• $T$ is the time to maturity of the forward contract in days

Understanding the Equation

The interest rate parity equation shows that the forward exchange rate ($F$) is determined by the current spot exchange rate ($S$), domestic interest rate ($r_{domestic}$), foreign interest rate ($r_{foreign}$), and the time to maturity of the forward contract ($T$). The formula indicates that the forward rate will either be at a premium or at a discount to the spot rate, depending on the interest rate differential between the two currencies.

Example: Suppose the current spot exchange rate between the US Dollar (USD) and the Euro (EUR) is 1.20 USD/EUR. The annual interest rate in the US is 3%, while in the Eurozone, it is 1.5%. We want to calculate the 180-day forward exchange rate. Using the interest rate parity formula:

$$F = 1.20 \times \left(1+\dfrac{0.03}{100} \right)^{\dfrac{180}{365}} \times \left(1+ \dfrac{0.015}{100} \right)^{-\dfrac{180}{365}} = 1.2042$$

Thus, the 180-day forward exchange rate is approximately 1.2042 USD/EUR, indicating a slight premium for the USD relative to the spot rate.