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Bounded Brownian Motion

Author

Listed:
  • Peter Carr

    (Department of Finance and Risk Engineering, Tandon School of Engineering, NYU, 12 MetroTech Center, Brooklyn, NY 11201, USA)

Abstract

Diffusions are widely used in finance due to their tractability. Driftless diffusions are needed to describe ratios of asset prices under a martingale measure. We provide a simple example of a tractable driftless diffusion which also has a bounded state space.

Suggested Citation

  • Peter Carr, 2017. "Bounded Brownian Motion," Risks, MDPI, vol. 5(4), pages 1-11, November.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:4:p:61-:d:119375
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    References listed on IDEAS

    as
    1. Peter P. Carr & Zura Kakushadze, 2017. "FX options in target zones," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1477-1486, October.
    2. Antoine Jacquier & Saad Slaoui, 2007. "Variance Dispersion and Correlation Swaps," Birkbeck Working Papers in Economics and Finance 0712, Birkbeck, Department of Economics, Mathematics & Statistics.
    3. Sven Rady, 1997. "Option pricing in the presence of natural boundaries and a quadratic diffusion term (*)," Finance and Stochastics, Springer, vol. 1(4), pages 331-344.
    4. C. H. Hui & C. F. Lo & V. Yeung & L. Fung, 2008. "Valuing foreign currency options with a mean-reverting process: a study of Hong Kong dollar," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 13(1), pages 118-134.
    5. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
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    Citations

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    Cited by:

    1. Albert Cohen & Nick Costanzino, 2017. "A General Framework for Incorporating Stochastic Recovery in Structural Models of Credit Risk," Risks, MDPI, vol. 5(4), pages 1-19, December.
    2. Brigo, Damiano & Jeanblanc, Monique & Vrins, Frédéric, 2020. "SDEs with uniform distributions: Peacocks, conic martingales and mean reverting uniform diffusions," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 3895-3919.
    3. Nassim Nicholas Taleb, 2017. "Election Predictions as Martingales: An Arbitrage Approach," Papers 1703.06351, arXiv.org, revised Jul 2019.
    4. Zura Kakushadze, 2020. "Option Pricing: Channels, Target Zones and Sideways Markets," Papers 2006.14121, arXiv.org.
    5. Cheikh Mbaye & Fr'ed'eric Vrins, 2019. "An arbitrage-free conic martingale model with application to credit risk," Papers 1909.02474, arXiv.org.
    6. Tianyao Chen & Xue Cheng & Jingping Yang, 2019. "Common Decomposition of Correlated Brownian Motions and its Financial Applications," Papers 1907.03295, arXiv.org, revised Nov 2020.
    7. László Márkus & Ashish Kumar, 2021. "Modelling Joint Behaviour of Asset Prices Using Stochastic Correlation," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 341-354, March.
    8. Albert Cohen, 2018. "Editorial: A Celebration of the Ties That Bind Us: Connections between Actuarial Science and Mathematical Finance," Risks, MDPI, vol. 6(1), pages 1-3, January.
    9. Samuel Drapeau & Yunbo Zhang, 2019. "Pricing and Hedging Performance on Pegged FX Markets Based on a Regime Switching Model," Papers 1910.08344, arXiv.org, revised May 2020.
    10. Zura Kakushadze, 2020. "Option Pricing: Channels, Target Zones and Sideways Markets," Bulletin of Applied Economics, Risk Market Journals, vol. 7(2), pages 25-33.

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