A functional analysis approach to the static replication of European options

Sébastien Bossu, Peter Carr, Andrew Papanicolaou

Research output: Contribution to journalArticlepeer-review


The replication of any European contingent claim by a static portfolio of calls and puts with strikes forming a continuum, formally proven by Carr and Madan [Towards a theory of volatility trading. In Volatility: New Estimation Techniques for Pricing Derivatives, edited by R.A. Jarrow, Vol. 29, pp. 417–427, 1998 (Risk books)], is part of the more general theory of integral equations. We use spectral decomposition techniques to show that exact payoff replication may be achieved with a discrete portfolio of special options. We discuss applications for fast pricing of vanilla options that may be suitable for large option books or high frequency option trading, and for model pricing when the characteristic function of the underlying asset price is known.

Original languageEnglish (US)
Pages (from-to)637-655
Number of pages19
JournalQuantitative Finance
Issue number4
StatePublished - 2021


  • Breeden-Litzenberger formula
  • Derivatives
  • Functional analysis
  • Implied distribution
  • Integral equation
  • Options
  • Payoff
  • Spectral theorem
  • Static replication

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance(all)


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