Measuring jump sizes in asset prices with an indirect approach

Abstract

The aim of this article is to estimate the magnitude of asset price jump sizes using an inverse method applied to historical financial data. Specifically, we adapt a particular form of the Merton jump-diffusion model for this estimation. The model is then discretized using the characteristics of the Poisson process along with the EulerMaruyama numerical method. Using historical financial data from various assets including global gold ounce prices, Alphabet (Google) stock, and crude oil collected over 2, 6, and 5-year periods, we estimate the price jump size for a short one-week time frame for these assets. This estimation is carried out by minimizing the price jump size inversely, using the discretized function obtained from the Euler-Maruyama numerical method, implemented through simulation in Python software. Finally, the effectiveness of the inverse method in estimating asset price jump sizes is evaluated by comparing the estimated values with the actual observed price jump sizes in the historical data of each asset, taking into account the calculated error.