Implementing short-rate models with jumps at deterministic times

Shibduth, Darvesh Yogandar

Implementing short-rate models with jumps at deterministic times

Master Thesis

2022

Abstract

Macroeconomic announcements have a direct impact on short-term interest rates during a financial year. However, this is not directly reflected in the continuous-time interest rate models. In this paper, we work with short-rate models which include the possibility of jumps at deterministic times. An application of the finite-difference method enables the pricing of bonds and bond options in these short-rate models with different types of jump distributions. A closed-form solution for bond prices, when the jumps are normally distributed, is available in the literature, but not for other jump distributions. The Monte Carlo method is used to compare the finite-difference calculations for these cases. An illustration of varying important model parameters is provided in which we observe that an increase in option prices could result from an increase in the jump variances and/or volatility parameters.

Keywords

finance

tax

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