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A generalized variance gamma process for financial applications

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  • Roberto Marfè

Abstract

In this work we propose a new multivariate pure jump model. We fully characterize a multivariate Lévy process with finite- and infinite-activity components in positive and negative jumps. This process generalizes the variance gamma process, featuring a ‘stochastic volatility’ effect due to Poisson randomized intensities of positive and negative gamma jumps. Linear and nonlinear dependence is introduced, without restrictions on marginal properties, separately on both positive and negative jumps and on both finite- and infinite-activity jumps. Such a new approach provides greater flexibility in calibrating nonlinear dependence than in other comparable Lévy models in the literature. The model is very tractable and a straightforward multivariate simulation procedure is available. An empirical analysis shows an almost perfect fit of option prices across a span of moneyness and maturities and a very accurate multivariate fit of stock returns in terms of both linear and nonlinear dependence. A sensitivity analysis of multi-asset option prices emphasizes the importance of the proposed new approach for modeling dependence.

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  • Roberto Marfè, 2012. "A generalized variance gamma process for financial applications," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 75-87, June.
  • Handle: RePEc:taf:quantf:v:12:y:2012:i:1:p:75-87 DOI: 10.1080/14697688.2010.505199
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    Cited by:

    1. Elisa Luciano & Marina Marena & Patrizia Semeraro, 2013. "Dependence Calibration and Portfolio Fit with FactorBased Time Changes," Carlo Alberto Notebooks 307, Collegio Carlo Alberto, revised 2015.
    2. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "Multivariate Skew-Normal Generalized Hyperbolic distribution and its properties," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 73-85.

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