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

Marco Avellaneda and Antonio ParAS

Applied Mathematical Finance, 1996, vol. 3, issue 1, 21-52

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.

Keywords: Uncertain volatility; dynamic hedging; hedging with options (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (33)

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DOI: 10.1080/13504869600000002

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