ABSTRACT
In this chapter we study lognormal approximations for Libor market models, proposed in Kurbanmuradov, Sabelfeld and Schoenmakers (2002), where special attention is paid to their simulation by direct methods and lognormal random fields. Generally, the main advantage of log-normal approximations is that their distributions can be simulated fast since, in contrast to the usual numerical solution of the Libor SDE, the approximations can be simulated directly at any future point in time. For instance, the lognormal approximation proposed in Brace, Gatarek and Musiela (1997) can be simulated effectively by a Gaussian random field of log-Libors. As a result, since in general valuation of Libor derivatives comes down to computation of expected values of functions of Libors, an important family of Libor instruments consisting of long dated exotic products can be valuated faster by using lognormal approximations. As such the proposed approximations provide valuable alternatives to the Euler method, in particular for long dated instruments.
