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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
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