# Interest Rate Parity

Interest rate parity refers to the fundamentally distinct features that associate exchange rates and interest rates. The distinctive feature is hypothetical in nature and commonly adopts the presumptions set forth in economic models.

There are proofs that substantiate and defy interest rate parity. Interest rate parity is a state of arbitrage that mentions the yield from obtaining one currency, changing over that currency to another currency, and making investment in interest rate securities with the help of the second currency and at the same time, buying future contracts for converting the currency again at the time of maturity period is equivalent to the yield from buying and retaining same types of interest rate securities with the help of the first currency. If the yield is not the same, the investors have the option of performing arbitrage on a theoretical basis and earn risk-free profit or gain.

From a different point of view, interest rate parity states the future prices and spot prices for foreign exchange trading comprise any type of interest rate deviations between two currencies.

Interest rate parity can be broadly categorized into the following types:

Covered interest rate parity
Covered interest rate parity is also known as interest parity condition. Covered interest rate parity can be described with the help of the following equation:
(1+i\$) = (F/S)(1+ic)

Here,

i\$ is the domestic rate of interest entailed for a debt of a certain maturity period
ic is the rate of interest in the overseas location for a debt with a similar maturity period
S refers to the spot exchange rate represented in the form of a domestic currency price (\$) of a single unit of the foreign exchange c, for example \$/c
F refers to the forward exchange rate entailed for a forward contract, which has a similar maturity period like the existing foreign debt and domestic debt i\$ and ic. F is represented with the help of similar units like S, for example, \$/c

Uncovered interest rate parity
The uncovered interest rate parity model can be described with the help of the following equation:
(1+i\$t, t+1) = Et[St+1] (1+ ict,t+1) / St

This model has the assumption that the risk premium is nil, however, this is applicable if the investment is risk-neural in nature.

Cost of carry model
This model is utilized for determining a commodity’s forward price, it uses compounded rates of interest on a continuous basis, and it can be described through the following equation:
F = Se(r+s-c)t

Here,

F refers to the forward price
S refers to the spot price
e refers to the natural logarithm base
r refers to the risk-free rate of interest
s refers to the storage expenses
c refers to the convenience yield
t refers to the delivery time of the forward contract transaction (represented in the form of a fraction of one year) 