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

Marco Avellaneda, Antonio ParÁS

Research output: Contribution to journalArticle

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 - Jan 1 1996

Fingerprint

Volatility
Derivatives
Derivative
Hedging
Heteroskedasticity
Partial differential equations
Equity
Nonlinear Partial Differential Equations
Model
Scenarios
Derivative securities
Volatility models
Volatility risk
Evaluate
Market
Liability
Nonlinear partial differential equations
Option hedging
Portfolio optimization
Foreign exchange

Keywords

  • dynamic hedging
  • hedging with options
  • Uncertain volatility

ASJC Scopus subject areas

  • Finance
  • Applied Mathematics

Cite this

Managing the volatility risk of portfolios of derivative securities : the Lagrangian uncertain volatility model. / Avellaneda, Marco; ParÁS, Antonio.

In: Applied Mathematical Finance, Vol. 3, No. 1, 01.01.1996, p. 21-52.

Research output: Contribution to journalArticle

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