## Glossary

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

# LIBOR

LIBOR London Interbank Offered Rate is the rate one London bank has to pay for an unsecured loan when borrowing from another London bank on the interbank market. Maturities are in the range from overnight up to one year. The rates are settled daily. They are usually published around 11.45 (AM) London time. Across the financial markets around the world there are similar arrangements (see XIBOR for a list of acronyms for LIBOR-like contracts).

## Definition of related contracts

SPOT LIBOR This contract gives the stochastic interest rate L[T,S], (the rate decided at time T), over the future time interval [T,S]. If we put in A units of currency at time T we get out A(1+(S-T)L[T,S]) at time S. We have that (1+(S-T)L[T,S])=1/p(T,S), where p(T,S) is the price of Zero coupon Bond issued at T with maturity S.
Forward rate agreement (FRA) The Forward rate agreement (FRA) contract swaps the floating LIBOR rate L[T,S] to the fixed rate K over the future time period [T,S]. Payoff (S-T)(L[T,S]-K). Price at time t for t≤T is
ΠFRAt([T,S],K)=(S-T)P(t,S)((p(t,T)-p(t,S))/((S-T)p(t,S))-K)
Forward LIBOR rate Lt[T,S] The fixed rate K that makes ΠFRAt([T,S],K)=0. i.e. Lt[T,S]=(p(t,T)-p(t,S))/((S-T)p(t,S)). Note that LT[T,S]=L[T,S].