Towards a $$\Delta $$Δ-Gamma Sato multivariate model

Lynn Boen () and Florence Guillaume ()
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Lynn Boen: University of Antwerp
Florence Guillaume: University of Antwerp

Review of Derivatives Research, 2020, vol. 23, issue 1, No 1, 39 pages

Abstract: Abstract The increased trading in multi-name financial products has paved the way for the use of multivariate models that are at once computationally tractable and flexible enough to mimic the stylized facts of asset log-returns and of their dependence structure. In this paper we propose a new multivariate Lévy model, the so-called $$\varDelta $$Δ-Gamma model, where the log-price gains and losses are modeled by separate multivariate Gamma processes, each containing a common and an idiosyncratic component. Furthermore, we extend this multivariate model to the Sato setting, allowing for a moment term structure that is more in line with empirical evidence. We calibrate the two models on single-name option price surfaces and market implied correlations and we show how the $$\varDelta $$Δ-Gamma Sato model outperforms its Lévy counterpart, especially during periods of market turmoil. The numerical study also reveals the advantages of these new types of multivariate models, compared to a multivariate VG model.

Keywords: Multi-name option pricing; Multivariate Lévy models; Multivariate models with Sato marginals; Difference of Gamma processes; Self-similar processes; Calibration (search for similar items in EconPapers)
JEL-codes: C51 C52 G12 G13 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11147-019-09155-y

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