Title: Asymmetric Laplace distribution jumps in continuous-time financial modelling
Authors: Matthew Stuart - Iowa State University (United States) [presenting]
Cindy Yu - Iowa State University (United States)
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, the volatility jumps are exponentially distributed, and the jumps occur either contemporaneously or independently, but not both. We propose to use an asymmetric Laplace distribution (ALD) to model jumps in returns and volatility (contemporaneous or independent) in order to overcome the drawback of lack of monotonicity in jump size density due to using a normal distribution with a negative mean. We also further the new research into cryptocurrency markets by proposing an ALD in returns in a 2-dimensional dataset, specifically on a market index and cryptocurrency, to examine the relationship between the assets. Monte Carlo Markov Chain (MCMC) methods 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 the S\&P 500 and Bitcoin independent and joint daily returns from 2014 to 2020.