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In this work we propose a new and general approach to build dependence in multivariate Lévy processes. We fully characterize a multivariate Lévy process whose margins are able to approximate any Lévy type. Dependence is generated by one or more common sources of jump intensity separately in jumps of any sign and size and a parsimonious method to determine the intensities of these common factors is proposed. Such a new approach allows the calibration of any smooth transition between independence and a large amount of linear dependence and provides greater flexibility in calibrating nonlinear dependence than in other comparable Lévy models in the literature. The model is analytically tractable and a straightforward multivariate simulation procedure is available. An empirical analysis shows an accurate multivariate fit of stock returns in terms of linear and nonlinear dependence. A numerical illustration of multi-asset option pricing emphasizes the importance of the proposed new approach for modeling dependence. [ABSTRACT FROM PUBLISHER]

In this work we propose a new approach to build multivariate pure jump processes. We introduce linear and nonlinear dependence, without restrictions on marginal properties, by imposing a multi-factorial structure separately on both positive and negative jumps. Such a new approach provides higher flexibility in calibrating nonlinear dependence than in other comparable Lévy models in the literature. Using the notion of multivariate subordinator, this modeling approach can be applied to the class of univariate Lévy processes which can be written as the difference of two subordinators. A common example in the financial literature is the variance gamma process, which we extend to the multivariate (multi-factorial) case. The model is tractable and a straightforward multivariate simulation procedure is available. An empirical analysis documents an accurate multivariate fit of stock index returns in terms of both linear and nonlinear dependence. An example of multi-asset option pricing emphasizes the importance of the proposed multivariate approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]