IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v13y2009i3p403-413.html
   My bibliography  Save this article

Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff

Author

Listed:
  • Michael Giles
  • Desmond Higham
  • Xuerong Mao

Abstract

No abstract is available for this item.

Suggested Citation

  • Michael Giles & Desmond Higham & Xuerong Mao, 2009. "Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff," Finance and Stochastics, Springer, vol. 13(3), pages 403-413, September.
    • Handle: RePEc:spr:finsto:v:13:y:2009:i:3:p:403-413
    DOI: 10.1007/s00780-009-0092-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00780-009-0092-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00780-009-0092-1?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. Higham,Desmond J., 2004. "An Introduction to Financial Option Valuation," Cambridge Books, Cambridge University Press, number 9780521547574.
    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. Ahmed Kebaier & Jérôme Lelong, 2018. "Coupling Importance Sampling and Multilevel Monte Carlo using Sample Average Approximation," Post-Print hal-01214840, HAL.
    2. Michael B. Giles & Kristian Debrabant & Andreas Ro{ss}ler, 2013. "Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation," Papers 1302.4676, arXiv.org, revised Jun 2019.
    3. Ahmed Kebaier & Jérôme Lelong, 2017. "Coupling Importance Sampling and Multilevel Monte Carlo using Sample Average Approximation," Working Papers hal-01214840, HAL.
    4. Andrei Cozma & Matthieu Mariapragassam & Christoph Reisinger, 2015. "Convergence of an Euler scheme for a hybrid stochastic-local volatility model with stochastic rates in foreign exchange markets," Papers 1501.06084, arXiv.org, revised Oct 2016.
    5. Dong An & Noah Linden & Jin-Peng Liu & Ashley Montanaro & Changpeng Shao & Jiasu Wang, 2020. "Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance," Papers 2012.06283, arXiv.org, revised Jun 2021.
    6. Michael B. Giles & Abdul-Lateef Haji-Ali & Jonathan Spence, 2023. "Efficient Risk Estimation for the Credit Valuation Adjustment," Papers 2301.05886, arXiv.org.
    7. Andrei Cozma & Christoph Reisinger, 2017. "Strong order 1/2 convergence of full truncation Euler approximations to the Cox-Ingersoll-Ross process," Papers 1704.07321, arXiv.org, revised Oct 2018.
    8. Michael B. Giles & Abdul-Lateef Haji-Ali, 2022. "Multilevel Path Branching for Digital Options," Papers 2209.03017, arXiv.org.
    9. Jean-Francois Chassagneux & Antoine Jacquier & Ivo Mihaylov, 2014. "An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients," Papers 1405.3561, arXiv.org, revised Apr 2016.
    10. Hoel Håkon & Tempone Raúl & von Schwerin Erik & Szepessy Anders, 2014. "Implementation and analysis of an adaptive multilevel Monte Carlo algorithm," Monte Carlo Methods and Applications, De Gruyter, vol. 20(1), pages 1-41, March.
    11. Andrei Cozma & Christoph Reisinger, 2017. "Strong convergence rates for Euler approximations to a class of stochastic path-dependent volatility models," Papers 1706.07375, arXiv.org, revised Oct 2018.
    12. Benjamin Jourdain & Mohamed Sbai, 2013. "High order discretization schemes for stochastic volatility models," Post-Print hal-00409861, HAL.
    13. Christian Bayer & Chiheb Ben Hammouda & Raul Tempone, 2020. "Multilevel Monte Carlo with Numerical Smoothing for Robust and Efficient Computation of Probabilities and Densities," Papers 2003.05708, arXiv.org, revised Oct 2023.
    14. Mouna Ben Derouich & Ahmed Kebaier, 2022. "The interpolated drift implicit Euler scheme Multilevel Monte Carlo method for pricing Barrier options and applications to the CIR and CEV models," Papers 2210.00779, arXiv.org.
    15. Hideyuki Tanaka & Toshihiro Yamada, 2013. "Strong Convergence for Euler-Maruyama and Milstein Schemes with Asymptotic Method (Forthcoming in "International Journal of Theoretical and Applied Finance")," CARF F-Series CARF-F-333, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    16. Ahmed Kebaier & Jérôme Lelong, 2018. "Coupling Importance Sampling and Multilevel Monte Carlo using Sample Average Approximation," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 611-641, June.
    17. Desmond J. Higham, 2015. "An Introduction to Multilevel Monte Carlo for Option Valuation," Papers 1505.00965, arXiv.org.
    18. Ahmed Kebaier & J'er^ome Lelong, 2015. "Coupling Importance Sampling and Multilevel Monte Carlo using Sample Average Approximation," Papers 1510.03590, arXiv.org, revised Jul 2017.
    19. Ben Alaya Mohamed & Kebaier Ahmed, 2014. "Multilevel Monte Carlo for Asian options and limit theorems," Monte Carlo Methods and Applications, De Gruyter, vol. 20(3), pages 181-194, September.
    20. Mike Giles & Lukasz Szpruch, 2012. "Multilevel Monte Carlo methods for applications in finance," Papers 1212.1377, arXiv.org.

    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. 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.
    2. Zhaojun Yang & Christian-Oliver Ewald & Yajun Xiao, 2009. "Implied Volatility From Asian Options Via Monte Carlo Methods," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 153-178.
    3. Qi Tang & Danni Yan, 2010. "Autoregressive trending risk function and exhaustion in random asset price movement," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 465-470, November.
    4. Kyoung-Sook Moon & Yunju Jeong & Hongjoong Kim, 2016. "An Efficient Binomial Method for Pricing Asian Options," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(2), pages 151-164.
    5. Somayeh Abdi-Mazraeh & Ali Khani & Safar Irandoust-Pakchin, 2020. "Multiple Shooting Method for Solving Black–Scholes Equation," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 723-746, December.
    6. Rambeerich, N. & Tangman, D.Y. & Lollchund, M.R. & Bhuruth, M., 2013. "High-order computational methods for option valuation under multifactor models," European Journal of Operational Research, Elsevier, vol. 224(1), pages 219-226.
    7. Geon Lee & Tae-Kyoung Kim & Hyun-Gyoon Kim & Jeonggyu Huh, 2022. "Newton Raphson Emulation Network for Highly Efficient Computation of Numerous Implied Volatilities," Papers 2210.15969, arXiv.org.
    8. Ömür Ugur, 2008. "An Introduction to Computational Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number p556, February.
    9. Avner Engel & Tyson R. Browning, 2008. "Designing systems for adaptability by means of architecture options," Systems Engineering, John Wiley & Sons, vol. 11(2), pages 125-146, June.
    10. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1, July-Dece.
    11. Abhishek Kumar & Ashwin Waikos & Siddhartha P. Chakrabarty, 2011. "Pricing of average strike Asian call option using numerical PDE methods," Papers 1106.1999, arXiv.org.
    12. Foad Shokrollahi, 2017. "Fractional delta hedging strategy for pricing currency options with transaction costs," Papers 1702.00037, arXiv.org.
    13. Xiang Wang & Jessica Li & Jichun Li, 2023. "A Deep Learning Based Numerical PDE Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 149-164, June.
    14. Desmond J. Higham, 2015. "An Introduction to Multilevel Monte Carlo for Option Valuation," Papers 1505.00965, arXiv.org.
    15. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2007.
    16. Melek AKSU & Şakir SAKARYA, 2018. "Pricing of Covered Warrants: An Analysis on Borsa İstanbul," Sosyoekonomi Journal, Sosyoekonomi Society.
    17. Geon Lee & Tae-Kyoung Kim & Hyun-Gyoon Kim & Jeonggyu Huh, 2022. "Newton–Raphson Emulation Network for Highly Efficient Computation of Numerous Implied Volatilities," JRFM, MDPI, vol. 15(12), pages 1-8, December.

    More about this item

    Keywords

    Barrier option; Complexity; Digital option; Euler–Maruyama; Lookback option; Path-dependent option; Statistical error; Strong error; Weak error; 65C05; 60H10; C15; C63;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    Statistics

    Access and download statistics

    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:spr:finsto:v:13:y:2009:i:3:p:403-413. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.