Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model

Marco Avellaneda, Antonio ParÁS

Research output: Contribution to journalArticlepeer-review

Abstract

We present an algorithm for hedging option portfolios and custom-tailored derivative securities, which uses options to manage volatility risk. The algorithm uses a volatility band to model heteroskedasticity and a non- linear partial differential equation to evaluate worst-case volatility scenarios for any given forward liability structure. This equation gives sub-additive portfolio prices and hence provides a natural ordering of prefer- ences in terms of hedging with options. The second element of the algorithm consists of a portfolio optim- ization taking into account the prices of options available in the market. Several examples are discussed, including possible applications to market-making in equity and foreign-exchange derivatives.

Original languageEnglish (US)
Pages (from-to)21-52
Number of pages32
JournalApplied Mathematical Finance
Volume3
Issue number1
DOIs
StatePublished - Mar 1996

Keywords

  • Uncertain volatility
  • dynamic hedging
  • hedging with options

ASJC Scopus subject areas

  • Finance
  • Applied Mathematics

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