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A matched asymptotic expansions approach to continuity corrections for discretely sampled options. Part 1: barrier options

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  • Sam Howison
  • Mario Steinberg

Abstract

We discuss the `continuity correction' that should be applied to relate the prices of discretely sampled barrier options and their continuously-sampled equivalents. Using a matched asymptotic expansions approach we show that the correction of Broadie, Glasserman \& Kou (\emph{Mathematical Finance} {\bf 7}, 325 (1997)) can be applied in a very wide variety of cases. We calculate the correction to higher order in terms of the expansion parameter (the scaled time between resets) and we show how to apply the correction in jump-diffusion and local volatility models.

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  • Sam Howison & Mario Steinberg, 2005. "A matched asymptotic expansions approach to continuity corrections for discretely sampled options. Part 1: barrier options," OFRC Working Papers Series 2005mf02, Oxford Financial Research Centre.
    • Handle: RePEc:sbs:wpsefe:2005mf02
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    File URL: http://www.finance.ox.ac.uk/file_links/finecon_papers/2005mf02.pdf
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    Cited by:

    1. Lord, Roger & Fang, Fang & Bervoets, Frank & Oosterlee, Kees, 2007. "A fast and accurate FFT-based method for pricing early-exercise options under Lévy processes," MPRA Paper 1952, University Library of Munich, Germany.

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