Managing the Volatility Risk of Portfolios of Derivative Securities: The Lagrangian Uncertain Volatility Model

Posted: 22 Aug 1998

See all articles by Marco Avellaneda

Marco Avellaneda

New York University (NYU) - Courant Institute of Mathematical Sciences; Finance Concepts LLC

Antonio Paras

New York University (NYU) - Courant Institute of Mathematical Sciences

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 preferences in terms of hedging with options. The second element of the algorithm consists of a portfolio optimization 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.

JEL Classification: G11

Suggested Citation

Avellaneda, Marco and Paras, Antonio, Managing the Volatility Risk of Portfolios of Derivative Securities: The Lagrangian Uncertain Volatility Model. Available at SSRN: https://ssrn.com/abstract=6884

Marco Avellaneda (Contact Author)

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

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Antonio Paras

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

New York University
New York, NY 10012
United States

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