American options under uncertain volatility

Adam Smith

Applied Mathematical Finance, 2002, vol. 9, issue 2, 123-141

Abstract: The uncertain volatility approach to financial derivatives is extended to American options (which allow early exercise before expiry). The requirement to model at the portfolio level made necessary by the non-linearity of the approach is found to lead to a recursive structure to the exercise possibilities across options. Other novel features include: the optimality sometimes of partial exercise; an interesting resolution to the issues surrounding short options whose exercise is controlled by a buyer counterparty; and the occurrence of a simple game structure for portfolios containing both long and short options. It is demonstrated that the exercise strategies resulting can significantly alter measured uncertain volatility risk. Contrary to the set of attributes for sensible risk measures put forward by Artzner, Delbaen, Eber and Heath, this risk need not be homogenous in portfolio size- forming a convincing argument for weakening this particular requirement.

Keywords: Optimal Exercise; Partial Exercise; Derivatives Risk Measurement (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (3)

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DOI: 10.1080/13504860210136730

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