Application of Kalman Filtering

Abstract

The aim of this work is to discuss the use of the Kalman lter in some economical problems. Generally taken, the Kalman lter is a mathematical method (an algorithm) used for estimation of the non-observable component of a state. Especially, this approach will be applied to estimate the risk-neutral state price density of CALL options. In such case a non-linear relation between state and observed variables may be assumed, and the problem has to be linearized by Taylor expansion. In detail, the main Kalman ltering in the simple linear case will be presented in the rst chapter. In the second chapter, you can nd some application of that Kalman ltering in case of CALL options. The study of the extended Kalman lter and its application in case of a nonlinear state model and the use of the Taylor expansion can be found in Chapter 3. In the fourth chapter, we will be talking about estimating the risk-neutral price density of a CALL option. The corresponding outputs from the program R and the most important results of this work are summarized in the last Chapter 5.