The multivariate Variance Gamma model: basket option pricing and calibration

Daniël Linders, Ben Stassen

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we propose a methodology for pricing basket options in the multivariate Variance Gamma model introduced in Luciano and Schoutens [Quant. Finance6(5), 385–402]. The stock prices composing the basket are modelled by time-changed geometric Brownian motions with a common Gamma subordinator. Using the additivity property of comonotonic stop-loss premiums together with Gauss-Laguerre polynomials, we express the basket option price as a linear combination of Black & Scholes prices. Furthermore, our new basket option pricing formula enables us to calibrate the multivariate VG model in a fast way. As an illustration, we show that even in the constrained situation where the pairwise correlations between the Brownian motions are assumed to be equal, the multivariate VG model can closely match the observed Dow Jones index options.

Original languageEnglish (US)
Pages (from-to)555-572
Number of pages18
JournalQuantitative Finance
Volume16
Issue number4
DOIs
StatePublished - Apr 2 2016
Externally publishedYes

Keywords

  • Basket option
  • Comonotonicity
  • Multivariate Variance Gamma
  • Multivariate calibration

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance(all)

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