Laplace Transform Identities for Diffusions, with Applications to Rebates and Barrier Options

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Laplace Transform Identities for Diffusions, with Applications to Rebates and Barrier Options

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Hardy Hulley () (School of Finance and Economics, University of Technology, Sydney)
Eckhard Platen () (School of Finance and Economics, University of Technology, Sydney)

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Abstract

Using a simple integral identity, we derive general expressions for the Laplace transform of the transition density of the process, if killing or reflecting boundaries are specified. We also obtain a number of useful expressions for the Laplace transforms of some functions of first-passage times for the diffusion. These results are applied to the special case of squared Bessel processes with killing or reflecting boundaries. In particular, we demonstrate how the above-mentioned integral identity enables us to derive the transition density of a squared Bessel process killed at the origin, without the need to invert a Laplace transform. Finally, as an application, we consider the problem of pricing barrier options on an index described by the minimal market model.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 203.

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Length: 23
Date of creation: 01 Oct 2007
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Handle: RePEc:uts:rpaper:203

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NEP-ALL-2007-10-20 (All new papers)

References listed on IDEAS
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Antoon Pelsser, 2000. "Pricing double barrier options using Laplace transforms," Finance and Stochastics, Springer, vol. 4(1), pages 95-104. [Downloadable!] (restricted)
David Heath & Eckhard Platen, 2002. "Consistent Pricing and Hedging for a Modified Constant Elasticity of Variance Model," Research Paper Series 78, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
Other versions:
- D. Heath & E. Platen, 2002. "Consistent pricing and hedging for a modified constant elasticity of variance model," Quantitative Finance, Taylor and Francis Journals, vol. 2(6), pages 459-467, June. [Downloadable!] (restricted)
Mark Craddock & David Heath & Eckhard Platen, 1999. "Numerical Inversion of Laplace Transforms: A Survey of Techniques with Applications to Derivative Pricing," Research Paper Series 27, Quantitative Finance Research Centre, University of Technology, Sydney.

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