Financial modelling applying multivariate Lévy processes: New insights into estimation and simulation

A.W. Rathgeber, J. Stadler and S. Stöckl

Physica A: Statistical Mechanics and its Applications, 2019, vol. 532, issue C

Abstract: In general, daily or intra-day stock returns are fat-tailed and heavily skewed. Lévy processes fulfil these modelling requirements and produce marginal distributions with finite variances. An extensive body of literature looks into the fittings and applications of single processes. In contrast, our analysis of multivariate Lévy models finds applications in pricing multivariate options or in portfolio and risk management. We use the technique of multivariate subordination and conduct a large simulation study on the fitting of the αρGH, αρNIG, and αρVG models in order to identify the best fitting method for multivariate Lévy processes, as well as the best multivariate model overall. Our findings confirm previous results in the literature, namely that the MLE is the best estimation approach in a two-step fitting procedure and the αρGH model is the best multivariate model. It reveals that also the χ2 method is appropriate.

Keywords: Multivariate Lévy processes; Fitting methods; Correlation estimation (search for similar items in EconPapers)
JEL-codes: C00 C02 C13 C15 G15 (search for similar items in EconPapers)
Date: 2019
References: Add references at CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:532:y:2019:i:c:s0378437119308064

DOI: 10.1016/j.physa.2019.121386

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