No-arbitrage interpolation of the option price function and its reformulation

Y. Wang, H. Yin, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)

Abstract

Several risk management and exotic option pricing models have been proposed in the literature which may price European options correctly. A prerequisite of these models is the interpolation of the market implied volatilities or the European option price function. However, the no-arbitrage principle places shape restrictions on the option price function. In this paper, an interpolation method is developed to preserve the shape of the option price function. The interpolation is optimal in terms of minimizing the distance between the implied risk-neutral density and the prior approximation function in L2-norm, which is important when only a few observations are available. We reformulate the problem into a system of semismooth equations so that it can be solved efficiently.
Original languageEnglish
Pages (from-to)627-649
Number of pages23
JournalJournal of Optimization Theory and Applications
Volume120
Issue number3
DOIs
Publication statusPublished - 1 Mar 2004

Keywords

  • Interpolation
  • No-arbitrage principle
  • Option price functions
  • Semismooth equations
  • Superlinear convergence

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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