Haitian
Scientific Society Seminar
Series

Sunday May 26, 2024

12:45-2:30

Zoom-Link: https://umassboston.zoom.us/j/94777986513

**An Exchange Rate Model Where the Fundamentals Follow
Jump Diffusion Processes **

**Jean René Cupidon **

**Misericordia University**

**Abstract****: **

This paper presents some models of exchange rate with jumps, namely jump diffusion ex- change rate models. Jump diffusion models are quite common in computational and theoretical Finance. It is known that exchange rates sometimes exhibit jumps during some time period. Therefore, it is important to take into account the presence of these jumps in exchange rate modeling in general, including exchange rate target zone modeling in particular. However, even the simplest jump diffusion model introduces some analytical difficulty in terms of finding analytical to the model. The models we analyze in this paper make use of Approximation Theory in order to come up with close form solutions to the underlying variables. This approach leads to the branch of Differential Equations called functional differential equations and more specifically the so-called Delay differential equations. Our approach leads to a second order Delay Differential Equation. Though, in principle, these types of functional differential Equations can be solved analytically in some cases, the task, in general, is quite enormous. We circumvent this technical difficulty by deriving an approximate solution using a power series expansion of the second order. Therefore, we derive a complete solution to the models and also investigate the model’s predictions of the exchange rate. We introduce two jump diffusion models. The first model examines the case where there are jumps with a constant magnitude. The second model considers the case of jumps of different sizes. These are relatively simpler cases to be analyzed. The more general setting would be to consider the possibility of random jumps. We do intend to tackle this situation here. We will present some computational aspects in terms of the difficulty often encountered in estimating these types of models. The difficulty increases for the type of exchange rate model being considered in this paper. Nevertheless, we will present some partial results. This is joint work with Judex Hyppolite (Simpson College).