Derivatives and Internal Models pp 343-356 | Cite as

# Forward Transactions on Interest Rates

Chapter

## Abstract

*A forward rate agreement*, abbreviated as

*FRA*, is a contract in which both contract parties agree to a fixed rate

*K*on a principal

*N*to be paid for some future interest period between

*T*and

*T*′. An. FRA can be interpreted as an agreement loan to be made in the future with an interest rate already fixed today The party receiving the loan makes the fixed interest payments. In contrast to bonds, we will refer to this party’s position as a

*long*position in the FRA, whereas the counterparty receiving the interest payments is

*short*in the FRA. A (long) FRA can thus be interpreted as an agreement on two future cash flows: a receipt of the principal

*N*at time

*T*(the loan is made) and a payment at maturity

*T*′ of the FRA in the amount of the principal

*N*compounded at the agreed rate

*K*over the period

*T*′ −

*T*(the loan plus interest is paid back). Both of these cash lows discounted back to time

*t*yield the present value of the FRA at time

*t*:

$${F_R}\left( {T,\;T',\;K|t} \right) = {\text{ }}{B_R}\left( {t,\;T} \right){\text{ }}\underbrace N_{{\text{Cash}}\;{\text{flow}}\;{\text{at}}\;{\text{time}}\;{\text{T}}}{\text{ }} - {B_R}\left( {t,\;T'} \right){\text{ }}\frac{N}{{\underbrace {{B_K}\left( {T,\;T'} \right)}_{{\text{Cash}}\;{\text{flow}}\;{\text{at}}\;{\text{time}}\;{\text{T'}}}}}{\text{ }} = {\text{ }}N{B_R}\left( {t,\;T} \right)\;\left[ {1 - \frac{{{B_R}\left( {T,\;T'|t} \right)}}{{{B_K}\left( {T,\;T'} \right)}}} \right]$$

(16.1)

*K*is chosen so that the contract is worthless at the time it is concluded. As can be deduced from Equation 16.1, this condition is satisfied when the fixed rate

*K*agreed upon in the FRA equals the

*forward rate*at time

*t*corresponding to the FRA period from

*T*until

*T*′.

## Preview

Unable to display preview. Download preview PDF.

## Copyright information

© Hans-Peter Deutsch 2009