Towards a Delta-Gamma Sato Multivariate Model

Boen, Lynn; Guillaume, Florence

doi:10.2139/ssrn.2900900

Cited by 3 publications

(8 citation statements)

References 21 publications

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“…Remark 4.1. These reduced multivariate difference of Gamma Lévy and Sato models are similar to the ∆-Gamma Lévy and Sato models proposed in [7], but with the extra condition on the difference of Gamma models that λ 1,j λ 2,j = λ 1,Z λ 2,Z = a j ∀j = 1, . .…”

Section: Some Specific Examplessupporting

confidence: 63%

“…Popular examples of one-sided tempered stable distributions in financial applications are the inverse Gaussian (IG) (α = 1 2 ) and the Gamma (α = 0) distributions, leading to a difference of IG and a difference of Gamma distributions, respectively (see also [13] or [22] and [7] for the use of difference of Gamma distributions in single-name and multi-name asset pricing models, respectively). The characteristic function of a Gamma(C, λ) and of an IG(C, λ) distribution is given by:…”

Section: Some Specific Examplesmentioning

confidence: 99%

“…Sato processes on the other hand, which are processes with time-inhomogeneous increments, exhibit moment term structures that are more in line with market observations. Moreover, they are better able at reproducing quoted option prices across both the strike and time-to-maturity dimensions, as illustrated in, for example, [7], [10] and [15].…”

Section: Introductionmentioning

confidence: 99%

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Building multivariate Sato models with linear dependence

Boen

Guillaume

2018

Quantitative Finance

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The increased trading in multi-name financial products has required the development of stateof-the-art multivariate models. These models should be computationally tractable and, at the same time, flexible enough to explain the stylized facts of asset log-returns and of their dependence structure. The popular class of multivariate Lévy models provides a variety of tractable models, but suffers from one major shortcoming: Lévy models can replicate single-name derivative prices for a given time-to-maturity, but not for the whole range of quoted strikes and maturities, especially during periods of market turmoil. Moreover, there is a significant discrepancy between the moment term structure of Lévy models and the one observed in the market. Sato processes on the other hand exhibit a moment term structure that is more in line with empirical evidence and allow for a better replication of single-name option price surfaces. In this paper, we propose a general framework for multivariate models characterized by independent and time-inhomogeneous increments, where the asset log-return processes at unit time are modeled as linear combinations of independent self-decomposable random variables, where at least one self-decomposable random variable is shared by all the assets. As examples, we consider two general subclasses within this new framework, where we assume a normal variance-mean mixture with a one-sided tempered stable mixing density or a difference of one-sided tempered stable laws for the distribution of the risk factors. Particular attention is given to the models' ability to explain the asset dependence structure. A numerical study reveals the advantages of these new types of models.

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Section: Some Specific Examplessupporting

confidence: 63%

Section: Some Specific Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Building multivariate Sato models with linear dependence

Boen

Guillaume

2018

Quantitative Finance

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“…To get around this shortcoming, Carr et al (2007) proposed the use of Sato processes, having a more realistic moment term structure, and Guillaume (2012) has shown that the Sato extension of the ↵ variance gamma introduced by Semeraro (2008) enhances marginal fit both for low-volatility and high-volatility regime periods, while preserving the correlation structure. These features are confirmed by Boen and Guillaume (2016) who introduce a multivariate extension of the di↵erence of Gamma processes by Finlay and Seneta (2008), in both Lévy and Sato versions.…”

Section: Introductionmentioning

confidence: 69%

“…Thus, we can calibrate the marginal parameters for both the Lévy and the corresponding Sato processes and compare the correlation spanned. Other approaches to model dependence -as the one in Marfè (2012) -could be considered, see, e.g., Boen and Guillaume (2016).…”

Section: Normal Inverse Gaussianmentioning

confidence: 99%

Multivariate Factor-Based Processes With Sato Margins

Marena

Romeo

Semeraro

2018

Int. J. Theor. Appl. Finan.

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We introduce a class of multivariate factor-based processes with the dependence structure of Lévy [Formula: see text]-models and Sato marginal distributions. We focus on variance gamma and normal inverse Gaussian marginal specifications for their analytical tractability and fit properties. We explore if Sato models, whose margins incorporate more realistic moments term structures, preserve the correlation flexibility in fitting option data. Since [Formula: see text]-models incorporate nonlinear dependence, we also investigate the impact of Sato margins on nonlinear dependence and its evolution over time. Further, the relevance of nonlinear dependence in multivariate derivative pricing is examined.

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Multivariate non-Gaussian models for financial applications

Bianchi,

Hitaj,

Tassinari

2020

Preprint

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In this paper we consider several continuous-time multivariate non-Gaussian models applied to finance and proposed in the literature in the last years. We study the models focusing on the parsimony of the number of parameters, the properties of the dependence structure, and the computational tractability. For each model we analyze the main features, we provide the characteristic function, the marginal moments up to order four, the covariances and the correlations. Thus, we describe how to calibrate them on the time-series of log-returns with a view toward practical applications and possible numerical issues. To empirically compare these models, we conduct an analysis on a five-dimensional series of stock index log-returns.

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Towards a Delta-Gamma Sato Multivariate Model

Cited by 3 publications

References 21 publications

Building multivariate Sato models with linear dependence

Building multivariate Sato models with linear dependence

Multivariate Factor-Based Processes With Sato Margins

Multivariate non-Gaussian models for financial applications

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