IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v124y2014i5p1881-1909.html
   My bibliography  Save this article

Approximations of non-smooth integral type functionals of one dimensional diffusion processes

Author

Listed:
  • Kohatsu-Higa, A.
  • Makhlouf, A.
  • Ngo, H.L.

Abstract

In this article, we obtain the weak and strong rates of convergence of time integrals of non-smooth functions of a one dimensional diffusion process. We propose the use of the exact simulation scheme to simulate the process at discretization points. In particular, we also present the rates of convergence for the weak and strong errors of approximation for the local time of a one dimensional diffusion process as an application of our method.

Suggested Citation

  • Kohatsu-Higa, A. & Makhlouf, A. & Ngo, H.L., 2014. "Approximations of non-smooth integral type functionals of one dimensional diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1881-1909.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:5:p:1881-1909
    DOI: 10.1016/j.spa.2014.01.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030441491400012X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2014.01.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Erhan Bayraktar & Virginia Young, 2010. "Optimal investment strategy to minimize occupation time," Annals of Operations Research, Springer, vol. 176(1), pages 389-408, April.
    2. Peter Carr & Vadim Linetsky, 2000. "The Valuation of Executive Stock Options in an Intensity-Based Framework," Review of Finance, European Finance Association, vol. 4(3), pages 211-230.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kulik, Alexei M., 2019. "On weak uniqueness and distributional properties of a solution to an SDE with α-stable noise," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 473-506.
    2. Altmeyer, Randolf & Chorowski, Jakub, 2018. "Estimation error for occupation time functionals of stationary Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1830-1848.
    3. Altmeyer, Randolf, 2023. "Central limit theorems for discretized occupation time functionals," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 101-125.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jun Ma, 2011. "Pricing of a reload employee stock option under severance risk," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1233-1244.
    2. Detemple, Jérôme & Laminou Abdou, Souleymane & Moraux, Franck, 2020. "American step options," European Journal of Operational Research, Elsevier, vol. 282(1), pages 363-385.
    3. Ming-Cheng Wu & I-Cheng Lin, 2013. "Determining fair values of performance-vested and forfeiture-embedded employee stock options," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 53(4), pages 1083-1106, December.
    4. Grasselli, Matheus & Henderson, Vicky, 2009. "Risk aversion and block exercise of executive stock options," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 109-127, January.
    5. Moawia Alghalith, 2012. "New stochastic calculus," Papers 1211.5819, arXiv.org.
    6. Yukihiro Tsuzuki, 2023. "Pitman's Theorem, Black-Scholes Equation, and Derivative Pricing for Fundraisers," Papers 2303.13956, arXiv.org.
    7. Alghalith, Moawia, 2012. "Forward dynamic utility functions: A new model and new results," European Journal of Operational Research, Elsevier, vol. 223(3), pages 842-845.
    8. Neofytos Rodosthenous & Hongzhong Zhang, 2017. "Beating the Omega Clock: An Optimal Stopping Problem with Random Time-horizon under Spectrally Negative L\'evy Models," Papers 1706.03724, arXiv.org.
    9. Tim Leung & Ronnie Sircar, 2009. "Accounting For Risk Aversion, Vesting, Job Termination Risk And Multiple Exercises In Valuation Of Employee Stock Options," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 99-128, January.
    10. Carmona, Julio & León, Angel & Vaello-Sebastià, Antoni, 2011. "Pricing executive stock options under employment shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 97-114, January.
    11. Philip Brown & Alex Szimayer, 2008. "Valuing executive stock options: performance hurdles, early exercise and stochastic volatility," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 48(3), pages 363-389, September.
    12. Tahir Choulli & Emmanuel Lepinette, 2024. "Super-hedging-pricing formulas and Immediate-Profit arbitrage for market models under random horizon," Papers 2401.05713, arXiv.org.
    13. Wang, Xingchun, 2021. "The values and incentive effects of options on the maximum or the minimum of the stock prices and market index," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    14. Dai, Min & Kwok, Yue Kuen & You, Hong, 2007. "Intensity-based framework and penalty formulation of optimal stopping problems," Journal of Economic Dynamics and Control, Elsevier, vol. 31(12), pages 3860-3880, December.
    15. Susana Álvarez-Díez & J. Baixauli-Soler & María Belda-Ruiz, 2014. "Are we using the wrong letters? An analysis of executive stock option Greeks," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 237-262, June.
    16. Iftikhar Ul Haq & Tanzeela Shaheen & Wajid Ali & Hamza Toor & Tapan Senapati & Francesco Pilla & Sarbast Moslem, 2023. "Novel Fermatean Fuzzy Aczel–Alsina Model for Investment Strategy Selection," Mathematics, MDPI, vol. 11(14), pages 1-23, July.
    17. repec:dau:papers:123456789/9550 is not listed on IDEAS
    18. Xiaoqing Liang & Virginia R. Young, 2020. "Minimizing the Probability of Lifetime Exponential Parisian Ruin," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 1036-1064, March.
    19. Konstandatos, Otto, 2020. "Fair-value analytical valuation of reset executive stock options consistent with IFRS9 requirements," Annals of Actuarial Science, Cambridge University Press, vol. 14(1), pages 188-218, March.
    20. Stacey Beaumont & Raluca Ratiu & David Reeb & Glenn Boyle & Philip Brown & Alexander Szimayer & Raymond Silva Rosa & David Hillier & Patrick McColgan & Athanasios Tsekeris & Bryan Howieson & Zoltan Ma, 2016. "Comments on Shan and Walter: ‘Towards a Set of Design Principles for Executive Compensation Contracts’," Abacus, Accounting Foundation, University of Sydney, vol. 52(4), pages 685-771, December.
    21. Vicky Henderson, 2005. "The impact of the market portfolio on the valuation, incentives and optimality of executive stock options," Quantitative Finance, Taylor & Francis Journals, vol. 5(1), pages 35-47.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:124:y:2014:i:5:p:1881-1909. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.