Hedging Interest Rate Derivatives (Evidence from Swaptions) in a Negative Interest Rate Environment: : A comparative analysis of Lognormal and Normal Model

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