Chen, Yuxin; Makarov, Roman N. Modelling asynchronous assets with jump-diffusion processes. (English) Zbl 1414.62416 Kilgour, D. Marc (ed.) et al., Recent advances in mathematical and statistical methods. IV AMMCS international conference, Waterloo, Canada, August 20–25, 2017. Cham: Springer. Springer Proc. Math. Stat. 259, 477-487 (2018). Summary: In this paper, we present a new multivariate jump-diffusion model for modelling financial securities that have missing or asynchronous data in time series of historical prices. The proposed model allows us to analyze a portfolio that combines a high-activity asset such as a market index (or an exchange-traded fund tracking a market index) and several low-activity assets. The model is constructed in such a way that low-activity assets correlate with each other only implicitly through the high-activity asset price process. To calibrate the model, we first estimate parameters of a high-activity asset and then estimate parameters for each low-activity asset by conditioning on the parameters of the high-activity asset. Here, we assume that the jump component follows a compound Poisson process, which is the same for all asset price processes. Two jump-size distributions are considered: the normal and the double-exponential probability distributions. We use the maximum likelihood method to estimate model parameters for different time-series datasets. The new models are compared with the model based on a multivariate Geometric Brownian motion.For the entire collection see [Zbl 1408.00020]. MSC: 62P05 Applications of statistics to actuarial sciences and financial mathematics 62H25 Factor analysis and principal components; correspondence analysis 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 91B84 Economic time series analysis Keywords:jump-diffusion; asset pricing; model calibration; missing data; maximum likelihood estimation; multivariate jump-diffusion model PDFBibTeX XMLCite \textit{Y. Chen} and \textit{R. N. Makarov}, Springer Proc. Math. Stat. 259, 477--487 (2018; Zbl 1414.62416) Full Text: DOI