Jakob Moberg presents his master's thesis

Calibration of short rate models with Finite difference schemes

Abstract

In this thesis the calibration of three one factor interest rate models is
studied. These models are:
- Black-Karasinski
- Black-Derman-Toy
- Hull-White
The method used is a numerical solver using a Crank-Nicholson discretization
scheme solving the term structure equation.
   The thesis starts with an introduction to the eld of interest rate
modelling in general and the three above mentioned models in particular.
It also presents necessary denitions and the Crank-Nicholson method
is examined. The problem with the absence of boundary conditions are
handled and action are taken to speed up the numerical calculations.
The problem of choosing loss function is discussed and using, ways of
replicating interest rate derivatives in a time consuming way is presented.
Comparison to other numerical schemes is done and finally calibration
results are presented.

Keywords: Crank-Nicholson, parameter calibration, short rate models,
cap, flooor, swaption, inversion of the yield curve, Black-Derman-Toy,
Black-Karasinski, Hull-White