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I. Basic math.
II. Pricing and Hedging.
1. Basics of derivative pricing I.
2. Change of numeraire.
3. Basics of derivative pricing II.
4. Market model.
A. Forward LIBOR.
B. LIBOR market model.
C. Swap rate.
D. Swap measure.
5. Currency Exchange.
6. Credit risk.
7. Incomplete markets.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Forward LIBOR.

et $t$ be observation time. We consider an agreement to invest at time $T$ , $T>t$ , a fixed amount of cash and collect at $T+\Delta$ , $\Delta>0$ , 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 $\alpha$ units 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 $T+\Delta$ when it pays 1 unit of currency. Therefore MATH We conclude that the fair rate for the contract is given by the relationship

MATH (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 $_{T+\Delta}$ .

Notation. Index. Contents.

Copyright 2007