Fitting-the-yield-curve-with-Kalman-Filter

This code replicates the Kalman filter algorithm for one factor CIR model as described in Bolder, David Jamieson, Affine Term-Structure Models: Theory and Implementation (October 2001). Available at SSRN: https://ssrn.com/abstract=1082826 or http://dx.doi.org/10.2139/ssrn.1082826

Kalman filter is an optimal estimation algorithm used to estimate states of a system when indirect measurement are present. The technique holds importance in control systems literature with wide scale implementation in navigation, tracking and computer vision.

However, as much powerful the KF is, it's power is less understood outside the engg. literature. The objective of this repository is to demonstrate the effectiveness of Kalman Filter as it estimates the term structure of interest rates. KF hold relevance here as the instantaneous short rates, used for estimation of term structur is unobservable.

Following are the constituting functions:

1. SimulateCIR.R : This function simulates the CIR term structure of interest rate with specified CIR parameters. The function returns monthly zero coupon rates for a period of 10 years.

2. LogLikelihoodCIR.R : This function returns the loglikelihood values of CIR parameters given the zero coupon rates.

3. MinimizeLL : This is the main function which calls the above two functions. The optimization function is iterated 200 times and the estimated CIR parameters is the mean of the 200 observations.

Result: Simulated and estimated CIR paramters obtained from the code are close, indicating Kalman filter to be an effective tool for estimating the term structure of interest rate.