IDEAS home Printed from https://ideas.repec.org/p/zbw/cpqfwp/15.html
   My bibliography  Save this paper

Latin hypercube sampling with dependence and applications in finance

Author

Listed:
  • Packham, Natalie
  • Schmidt, Wolfgang M.

Abstract

In Monte Carlo simulation, Latin hypercube sampling (LHS) [McKay et al. (1979)] is a well-known variance reduction technique for vectors of independent random variables. The method presented here, Latin hypercube sampling with dependence (LHSD), extends LHS to vectors of dependent random variables. The resulting estimator is shown to be consistent and asymptotically unbiased. For the bivariate case and under some conditions on the joint distribution, a central limit theorem together with a closed formula for the limit variance are derived. It is shown that for a class of estimators satisfying some monotonicity condition, the LHSD limit variance is never greater than the corresponding Monte Carlo limit variance. In some valuation examples of financial payoffs, when compared to standard Monte Carlo simulation, a variance reduction of factors up to 200 is achieved. LHSD is suited for problems with rare events and for high-dimensional problems, and it may be combined with Quasi-Monte Carlo methods.

Suggested Citation

  • Packham, Natalie & Schmidt, Wolfgang M., 2008. "Latin hypercube sampling with dependence and applications in finance," CPQF Working Paper Series 15, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
  • Handle: RePEc:zbw:cpqfwp:15
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/40177/1/58176224X.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Ansgar Belke & Thorsten Polleit, 2005. "(How) Do Stock Market Returns React to Monetary Policy? - An ARDL Cointegration Analysis for Germany," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 253/2005, Department of Economics, University of Hohenheim, Germany.
    2. Ansgar Belke & Thorsten Polleit, 2007. "How the ECB and the US Fed set interest rates," Applied Economics, Taylor & Francis Journals, vol. 39(17), pages 2197-2209.
    3. Hirsch, Christian & Bannier, Christina E., 2007. "The economics of rating watchlists: Evidence from rating changes," CFS Working Paper Series 2008/02, Center for Financial Studies (CFS).
    4. Christina Bannier, 2007. "Heterogeneous multiple bank financing: does it reduce inefficient credit-renegotiation incidences?," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 21(4), pages 445-470, December.
    5. Wollersheim, Jutta & Barthel, Erich, 2008. "Kulturunterschiede bei Mergers & Acquisitions: Entwicklung eines Konzeptes zur Durchführung einer Cultural Due Diligence," Frankfurt School - Working Paper Series 94, Frankfurt School of Finance and Management.
    6. Bannier, Christina E. & Hänsel, Dennis N., 2007. "Determinants of banks' engagement in loan securitization," Frankfurt School - Working Paper Series 85, Frankfurt School of Finance and Management.
    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. Inklaar, Robert & Koetter, Michael & Noth, Felix, 2012. "Who's afraid of big bad banks? Bank competition, SME, and industry growth," Frankfurt School - Working Paper Series 197, Frankfurt School of Finance and Management.
    2. Dietmar Harhoff & Elisabeth Mueller & John Reenen, 2014. "What are the Channels for Technology Sourcing? Panel Data Evidence from German Companies," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 23(1), pages 204-224, March.
    3. Boeing, Philipp & Mueller, Elisabeth & Sandner, Philipp, 2012. "What makes Chinese firms productive? Learning from indigenous and foreign sources of knowledge," Frankfurt School - Working Paper Series 196, Frankfurt School of Finance and Management.
    4. Kostka, Genia & Moslener, Ulf & Andreas, Jan G., 2011. "Barriers to energy efficiency improvement: Empirical evidence from small-and-medium sized enterprises in China," Frankfurt School - Working Paper Series 178, Frankfurt School of Finance and Management.
    5. Alexander Libman & Vladimir Kozlov & André Schultz, 2012. "Roving Bandits in Action: Outside Option and Governmental Predation in Autocracies," Kyklos, Wiley Blackwell, vol. 65(4), pages 526-562, November.
    6. Yu, Xiaofan, 2011. "A spatial interpretation of the persistency of China's provincial inequality," Frankfurt School - Working Paper Series 171, Frankfurt School of Finance and Management.
    7. Georg Mainik, 2015. "Risk aggregation with empirical margins: Latin hypercubes, empirical copulas, and convergence of sum distributions," Papers 1508.02749, arXiv.org.
    8. Arbenz, Philipp & Hummel, Christoph & Mainik, Georg, 2012. "Copula based hierarchical risk aggregation through sample reordering," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 122-133.
    9. Böing, Philipp & Müller, Elisabeth, 2012. "Technological Capabilities of Chinese Enterprises: Who is Going to Compete Abroad?," Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62081, Verein für Socialpolitik / German Economic Association.

    More about this item

    Keywords

    Monte Carlo simulation; variance reduction; Latin hypercube sampling; stratified sampling;

    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
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    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:zbw:cpqfwp:15. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics). General contact details of provider: http://edirc.repec.org/data/hfbfide.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.