This thesis is about hedging interest rate derivatives in a negative interest rate environment.

The main focus is on doing a comparative analysis on how risk varies between Lognormal

and Normal models. This because Lognormal models do not work in the negative interest rate

since they do not allow negative values, hence there is a need of using Normal models. The

use of different models will yield identical price but different hedges. In order to study this

we looked at the case of Swaptions and Swaps as an example of interest rate derivatives. To

study risk in these two models we employed the method of risk matrices to measure and report

risk. We created various risk matrices for both Black model and Normal Black model which

included the price matrices, Delta and Vega matrices to study how Swaptions and Swaps with

different maturities are sensitive to changes in different parameters. We also plotted how Delta

and Vega vary between the two models.