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Density of Skew Brownian motion and its functionals with application in finance

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  • Alexander Gairat
  • Vadim Shcherbakov

Abstract

We derive the joint density of a Skew Brownian motion, its last visit to the origin, local and occupation times. The result is applied to option pricing in a two valued local volatility model and in a displaced diffusion model with constrained volatility.

Suggested Citation

  • Alexander Gairat & Vadim Shcherbakov, 2014. "Density of Skew Brownian motion and its functionals with application in finance," Papers 1407.1715, arXiv.org, revised Mar 2015.
    • Handle: RePEc:arx:papers:1407.1715
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    References listed on IDEAS

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    1. Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2004. "Applications of δ-function perturbation to the pricing of derivative securities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(3), pages 677-692.
    2. Marc Decamps & Marc Goovaerts & Wim Schoutens, 2006. "Self Exciting Threshold Interest Rates Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(07), pages 1093-1122.
    3. Viatcheslav Gorovoi & Vadim Linetsky, 2004. "Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 49-78, January.
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