Pricing options on realized variance

Peter Carr, Hélyette Geman, Dilip B. Madan, Marc Yor

Research output: Contribution to journalArticlepeer-review

Abstract

Models which hypothesize that returns are pure jump processes with independent increments have been shown to be capable of capturing the observed variation of market prices of vanilla stock options across strike and maturity. In this paper, these models are employed to derive in closed form the prices of derivatives written on future realized quadratic variation. Alternative work on pricing derivatives on quadratic variation has alternatively assumed that the underlying returns process is continuous over time. We compare the model values of derivatives on quadratic variation for the two types of models and find substantial differences.

Original languageEnglish (US)
Pages (from-to)453-475
Number of pages23
JournalFinance and Stochastics
Volume9
Issue number4
DOIs
StatePublished - Oct 2005

Keywords

  • Options on time changes
  • Options on variance swaps
  • Self decomposability and its hierarchy

ASJC Scopus subject areas

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty

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