Pricing multivariate barrier reverse convertibles with factor-based subordinators

Marina Marena; Andrea Romeo; Patrizia Semeraro

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We investigate the link between marginal distributions and correlation structure in a class of multivariate Lévy models, the ρα models, showing how the range of the correlation spanned by the model depends on the process marginal distributions.
We examine the pricing performance of ρα models with regard to barrier reverse convertibles, one of the most popular segments of the Swiss market. A sensitivity analysis quantiﬁes the impact of model parameters on prices and allows us to assess the relative importance of correlation structure and marginal processes, given the characteristics in terms of barrier and maturity of the contract.
We empirically ﬁnd a trade-oﬀ between marginal and correlation ﬁt. In particular, a joint calibration of the marginal distributions and the correlation structure may be required to obtain an overall accurate model ﬁt.
We show that the correlation can play a signiﬁcant role in pricing long term MBRCs. This feature requires a good correlation ﬁt.

Abstract

In this paper, we study factor-based subordinated Lévy processes in their variance gamma (VG) and normal inverse Gaussian (NIG) specifications, and focus on their ability to price multivariate exotic derivatives. Both model specifications, calibrated to a data set of multivariate barrier reverse convertibles listed at the Swiss market, demonstrate good ability in capturing smile patterns and recovering empirical correlations. We show how the range of correlations spanned by each model is linked to the process marginal distributions. Our analysis finds that a trade-off exists between marginal and correlation fit. A sensitivity analysis is performed, showing how a product’s characteristics and a model’s features affect multibarrier reverse convertibles prices. Market and model prices are analyzed, and discrepancies are highlighted and explained.

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