Static hedging of standard options

Peter Carr, Liuren Wu

Research output: Contribution to journalArticlepeer-review

Abstract

Working in a single-factor Markovian setting, this article derives a new, static spanning relation between a given option and a continuum of shorter-term options written on the same asset. Compared to dynamic delta hedge, which breaks down in the presence of large random jumps, the static hedge works well under both continuous and discontinuous price dynamics. Simulation exercises show that under purely continuous price dynamics, discretized static hedges with as few as three to five options perform similarly to the dynamic delta hedge with the underlying futures and daily updating, but the static hedges strongly outperform the daily delta hedge when the underlying price process contains random jumps. A historical analysis using over 13 years of data on S&P 500 index options further validates the superior performance of the static hedging strategy in practical situations.

Original languageEnglish (US)
Article numbernbs014
Pages (from-to)3-46
Number of pages44
JournalJournal of Financial Econometrics
Volume12
Issue number1
DOIs
StatePublished - Dec 2013

Keywords

  • Jumps
  • Monte carlo
  • Option pricing
  • S&P 500 index options
  • Static hedging
  • Stochastic volatility

ASJC Scopus subject areas

  • Finance
  • Economics and Econometrics

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