TRACKING ERRORS FROM DISCRETE HEDGING IN EXPONENTIAL LÉVY MODELS

Mats Brodén () and Peter Tankov ()
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Mats Brodén: Centre for Mathematical Sciences, Lund University, 22100 Lund, Sweden
Peter Tankov: Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau Cedex, France

International Journal of Theoretical and Applied Finance (IJTAF), 2011, vol. 14, issue 06, 803-837

Abstract: We analyze the errors arising from discrete readjustment of the hedging portfolio when hedging options in exponential Lévy models, and establish the rate at which the expected squared error goes to zero when the readjustment frequency increases. We compare the quadratic hedging strategy with the common market practice of delta hedging, and show that for discontinuous option pay-offs the latter strategy may suffer from very large discretization errors. For options with discontinuous pay-offs, the convergence rate depends on the underlying Lévy process, and we give an explicit relation between the rate and the Blumenthal-Getoor index of the process.

Keywords: Exponential Lévy models; quadratic hedging; delta hedging; discretization error; L2 convergence; digital options (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1142/S0219024911006760

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