Dissertation on Markov Functional Term Structure Model
Semi-analytic Lattice Integration of a Markov Functional Term Structure Model One frequent use of Markov functional models is to estimated LIBOR market models and to avoid complications the terminal forward measure is naturally used. If this method is applied to long term structures (ten or more years), the distribution of the early LIBORs in the term structure has a very large tail, which is usually not completely captured by common numerical techniques (either Monte Carlo or grid-based methods).
A numerical method that is regularly applied to Markov functional models is known as the semi-analytic lattice integrator (Sali) tree. This thesis examines the implications of the long tails on the Sali tree. Adequate boundary conditions and grid sizes are derived in order to capture the effect of the long tails. It turns out that this method either exhibits stability problems or demands for relatively small lattice spacing. The reason for this is examined in detail and several variations of the Sali tree to avoid this effect are suggested and analyzed. Furthermore the optimization of the grid parameters is considered in order to reduce the necessary computation time.
