The multivariate black & scholes market: Conditions for completeness and no-arbitrage

J. Dhaene, A. Kukush, Daniel Hemant Linders

Research output: Contribution to journalArticle

Abstract

In order to price multivariate derivatives, there is need for a multivariate stock price model. To keep the simplicity and attractiveness of the one-dimensional Black & Scholes model, one often considers a multivariate model where each individual stock follows a Black & Scholes model, but the underlying Brownian motions might be correlated. Although the classical one-dimensional Black & Scholes model is always arbitrage-free and complete, this statement does not hold true in a multivariate setting. In this paper, we derive conditions under which the multivariate Black & Scholes model is arbitrage-free and complete.

Original languageEnglish (US)
Pages (from-to)85-98
Number of pages14
JournalTheory of Probability and Mathematical Statistics
Volume88
DOIs
StatePublished - 2014
Externally publishedYes

Keywords

  • Arbitrage-free
  • Black & Scholes
  • Brownian motion
  • Completeness
  • Multivariate asset price models
  • Risk-neutral probability measure

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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