Forward LIBOR.

uppose at time $t$ we consider an agreement to invest at $T$ a fixed amount of cash and collect at $T+\Delta$ one unit of reference currency. We denote MATH the simple compounding rate during the time interval MATH implied by such a contract. We replicate this contract by selling $\alpha$ unit of bond MATH and purchasing one unit of bond MATH . If the implied rate MATH is fair then the contract should not worth anything at time $t$ : MATH The cash flow at time $T$ is $-\alpha$ . According to the contract the investment will grow at the rate MATH up to the time $T+\Delta$ , hence MATH We conclude that the fair rate for the contract is given by the relationship

(Libor)

By definition, this is the "forward LIBOR". The structure of the last formula is such that the rate MATH is a $t-$ martingale with respect to the MATH forward probability measure Prob MATH Prob $_{T+\Delta}$ .

Forum

Notation

Index

Contents