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Multivariate downside risk: Normal versus Variance Gamma
Author(s) -
Wallmeier Martin,
Diethelm Martin
Publication year - 2012
Publication title -
journal of futures markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.88
H-Index - 55
eISSN - 1096-9934
pISSN - 0270-7314
DOI - 10.1002/fut.20539
Subject(s) - multivariate statistics , univariate , subordinator , stylized fact , econometrics , multivariate analysis of variance , downside risk , economics , multivariate analysis , variance (accounting) , asset (computer security) , financial economics , mathematics , brownian motion , computer science , statistics , portfolio , accounting , computer security , macroeconomics
Abstract Although several types of options on multiple assets are popular in today's financial markets, valuing multiasset options is still a challenge in finance. The standard framework of multivariate normality is often inappropriate, since it ignores fat tails and other stylized facts of asset returns. The variance gamma (VG) model appears to be a promising alternative. In the univariate case, it has become a standard tool in finance. The traditional way to extend the model to the multivariate case is to subordinate a Brownian motion through a univariate subordinator. In recent years, generalizations with multivariate subordinators have been proposed. Our objective is to study two versions of the multivariate VG model in a large‐scale application with multiasset options traded in an active market. Our database consists of 468 multivariate barrier reverse convertibles at the Swiss market for structured products. The Swiss market ranks among the largest in the world and is characterized by an exceptional popularity of multiple asset options. We find that there is a trade‐off between the two VG models considered: one performs better in capturing the smile, the other is more often able to capture the correlation structure. In all, based on our calibration, only 316 of 468 products can be evaluated with at least one of the two VG models. We conclude that there is a need for more flexible extensions. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark