Contingent claims and market completeness in a stochastic volatility model

Marc Romano, Nizar Touzi

Research output: Contribution to journalArticlepeer-review


In an incomplete market framework, contingent claims are of particular interest since they improve the market efficiency. This paper addresses the problem of market completeness when trading in contingent claims is allowed. We extend recent results by Bajeux and Rochet (1996) in a stochastic volatility model to the case where the asset price and its volatility variations are correlated. We also relate the ability of a given contingent claim to complete the market to the convexity of its price function in the current asset price. This allows us to state our results for general contingent claims by examining the convexity of their "admissible arbitrage prices.".

Original languageEnglish (US)
Pages (from-to)399-412
Number of pages14
JournalMathematical Finance
Issue number4
StatePublished - Oct 1997


  • Incomplete market
  • Maximum principle
  • Partial differential equations

ASJC Scopus subject areas

  • Accounting
  • Social Sciences (miscellaneous)
  • Finance
  • Economics and Econometrics
  • Applied Mathematics


Dive into the research topics of 'Contingent claims and market completeness in a stochastic volatility model'. Together they form a unique fingerprint.

Cite this