Joint modeling of VIX and SPX options at a single and common maturity with risk management applications

Peter Carr, Dilip B. Madan

Research output: Contribution to journalArticle

Abstract

A double gamma model is proposed for the VIX. The VIX is modeled as gamma distributed with a mean and variance that respond to a gamma-distributed realized variance over the preceeding month. Conditional on VIX and the realized variance, the logarithm of the stock is variance gamma distributed with affine conditional drift and quadratic variation. The joint density for the triple realized variance, VIX, and the SPX is in closed form. Maximum likelihood estimation on time series data addresses model adequacy. A joint calibration of the model to SPX and VIX options is employed to illustrate a risk management application hedging realized volatility options. © 2014

Original languageEnglish (US)
Pages (from-to)1125-1131
Number of pages7
JournalIIE Transactions (Institute of Industrial Engineers)
Volume46
Issue number11
DOIs
StatePublished - Nov 2 2014

Keywords

  • Ask price minimizing hedge
  • distorted expectation
  • variance gamma model

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering

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