Estimation of Asset Models with Stochastic Volatility and Asymmetric Laplacian Jumps and Its Application to Cryptocurrency

• Activity Number: 405 - Winners: Business and Economic Statistics Student Paper Awards
• Type: Topic-Contributed
• Date/Time: Thursday, August 12, 2021 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Matthew Stuart* and Cindy Yu and Lendie Follett
• Companies: Iowa State University and Iowa State University and Drake University
• Keywords: cryptocurrency; Bitcoin; asymmetric Laplace; stochastic volatility; financial markets; MCMC

Abstract

In the existing continuous time finance literature with jumps in returns and stochastic volatility (SV), it is often assumed that the return jumps are normally distributed with a negative mean. In this paper, we propose to use an asymmetric Laplace distribution (ALD) to model jumps in returns to overcome the drawback of lack of monotonicity in jump size density due to using normal distribution with a negative mean. We also further the new research by proposing bivariate ALD jumps in returns (on either one or both assets) in a 2-dimensional dataset, specifically on a market index and cryptocurrency, to examine the relationship between the assets. The proposed jump process is flexible to allow for both independent jump times and contemporaneous jump times in the same model. Monte Carlo Markov Chain (MCMC) methods with the particle Gibbs with ancestor sampling (PGAS) algorithm are developed to estimate the model parameters and latent state variables, such as SV, jump times, jump sizes, and is validated through simulation studies. The method is applied to fit both daily returns of S&P 500 and Bitcoin independently and jointly from 2014 to 2020.