Performance analysis of Zero Black-Derman-Toy interest rate model in catastrophic events: COVID-19 case study

TL;DR

This paper evaluates the Zero Black-Derman-Toy interest rate model, which incorporates jumps to near-zero rates, to better assess financial derivatives during catastrophic events like COVID-19, comparing it with the classical BDT model.

Contribution

The paper introduces the ZBDT model with jump features, extending the classical BDT model, and demonstrates its application in pandemic-related economic scenarios.

Findings

ZBDT better captures interest rate jumps during crises.

Valuation differences between ZBDT and BDT models are significant in downturns.

Application to US sovereign bonds during COVID-19 highlights model effectiveness.

Abstract

In this paper we continue the research of our recent interest rate tree model called 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 to better match to risk of financial slowdown caused by catastrophic events. We present how to valuate a wide range of financial derivatives for such a model. The classical Black-Derman-Toy (BDT) model and 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 of them is the hypothetical case of an S-shape term structure and decreasing volatility of yields. The second case is an application of the ZBDT model in the structure of United States sovereign bonds in the current $2020$ 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 different derivatives.