Who gains all his ends did set the level too low. Although the history
of trading on financial markets started a long and possibly not exactly
definable time ago, most financial analysts agree that the core of
mathematical finance dates back to the year 1973. Not only did the
world's first option exchange open its doors in Chicago in that year but
Black and Scholes published their pioneering paper [BS73] on the
pricing and hedging of contingent claims. Since then their explicit
pricing formula has become the market standard for pricing European
stock op- tions and related financial derivatives. In contrast to the
equity market, no comparable model is accepted as standard for the
interest-rate market as a whole. One of the reasons is that
interest-rate derivatives usually depend on the change of a complete
yield curve rather than only one single interest rate. This complicates
the pricing of these products as well as the process of managing their
market risk in an essential way. Consequently, a large number of
interest-rate models have appeared in the literature using one or more
factors to explain the potential changes of the yield curve. Beside the
Black ([Bla76]) and the Heath-Jarrow-Morton model ([HJM92]) which
are widely used in practice, the LIBOR and swap market models introduced
by Brace, G tarek, and Musiela [BGM97], Miltersen, Sandmann, and Son-
dermann [MSS97J, and Jamshidian [Jam98] are among the most promising
ones.
