Zero Black-Derman-Toy Model in Catastrophic Events: COVID-19 Performance Analysis

Abstract

In this article, we continue the research of our recent interest rate tree model, called the Zero Black-Derman-Toy (ZBDT) model, which includes the possibility of a jump at each step to a practically zero interest rate. This approach allows a better match with the risk of financial slowdown caused by catastrophic events. We present how to valuate a wide range of financial derivatives using such a model. The classical Black-Derman-Toy (BDT) model and a novel ZBDT model are described, and analogies in their calibration methodology are established. Finally, two cases of applications of the novel ZBDT model are introduced. The first is the hypothetical case of an S-shaped term structure and decreasing volatility of yields. The second case is an application in the structure of US sovereign bonds in the 2020 economic slowdown caused by the coronavirus pandemic. The objective of this study is to understand the differences presented by the valuation in both models for exotic derivatives.