A functional analysis approach to the static replication of European options. Issue 4 (3rd April 2021)

• Record Type: Journal Article
• Authors: Bossu, Sébastien; Carr, Peter; Papanicolaou, Andrew
• Is Part Of: Quantitative finance. Volume 21:Issue 4(2021)
• Page Start: 637
• Page End: 655
• Publication Date: 2021-04-03
• Subjects: Derivatives -- Options -- Static replication -- Payoff -- Integral equation -- Functional analysis -- Spectral theorem -- Breeden-Litzenberger formula -- Implied distribution; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2020.1810857
• Languages: English
• ISSNs: 1469-7688

Abstract

Abstract : 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.