IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v12y2012i10p1571-1583.html
   My bibliography  Save this article

A new method for generating approximation algorithms for financial mathematics applications

Author

Listed:
  • Frank J. Fabozzi
  • Arturo Leccadito
  • Radu S. Tunaru

Abstract

This paper describes a new technique that can be used in financial mathematics for a wide range of situations where the calculation of complicated integrals is required. The numerical schemes proposed here are deterministic in nature but their proof relies on known results from probability theory regarding the weak convergence of probability measures. We adapt those results to unbounded payoffs under certain mild assumptions that are satisfied in finance. Because our approximation schemes avoid repeated simulations and provide computational savings, they can potentially be used when calculating simultaneously the price of several derivatives contingent on the same underlying. We show how to apply the new methods to calculate the price of spread options and American call options on a stock paying a known dividend. The method proves useful for calculations related to the log-Weibull model proposed recently for empirical asset pricing.

Suggested Citation

  • Frank J. Fabozzi & Arturo Leccadito & Radu S. Tunaru, 2012. "A new method for generating approximation algorithms for financial mathematics applications," Quantitative Finance, Taylor & Francis Journals, vol. 12(10), pages 1571-1583, October.
    • Handle: RePEc:taf:quantf:v:12:y:2012:i:10:p:1571-1583
    DOI: 10.1080/14697688.2011.580363
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697688.2011.580363
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697688.2011.580363?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. Peter Carr & Michael Schroder, 2001. "On the valuation of arithmetic-average Asian options: the Geman-Yor Laplace transform revisited," Papers math/0102080, arXiv.org.
    2. Evans, Michael & Swartz, Timothy, 2000. "Approximating Integrals via Monte Carlo and Deterministic Methods," OUP Catalogue, Oxford University Press, number 9780198502784.
    Full references (including those not matched with items on IDEAS)

    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. repec:jss:jstsof:33:i11 is not listed on IDEAS
    2. Episcopos, Athanasios, 2004. "The implied reserves of the Bank Insurance Fund," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1617-1635, July.
    3. Nott, David J. & Fielding, Mark & Leonte, Daniela, 2009. "On a generalization of the Laplace approximation," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1397-1403, June.
    4. Berridge, S.J. & Schumacher, J.M., 2002. "An Irregular Grid Approach for Pricing High Dimensional American Options," Other publications TiSEM 416a6d43-3466-47e0-b656-d, Tilburg University, School of Economics and Management.
    5. A. Kong & P. McCullagh & X.‐L. Meng & D. Nicolae & Z. Tan, 2003. "A theory of statistical models for Monte Carlo integration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 585-604, August.
    6. Fakhereddine, Rana & Haddad, Rami El & Lécot, Christian & Maalouf, Joseph El, 2017. "Stratified Monte Carlo simulation of Markov chains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 135(C), pages 51-62.
    7. Roberto Patuelli & Daniel A. Griffith & Michael Tiefelsdorf & Peter Nijkamp, 2011. "Spatial Filtering and Eigenvector Stability: Space-Time Models for German Unemployment Data," International Regional Science Review, , vol. 34(2), pages 253-280, April.
    8. Henry Lam & Jose Blanchet & Damian Burch & Martin Z. Bazant, 2011. "Corrections to the Central Limit Theorem for Heavy-tailed Probability Densities," Journal of Theoretical Probability, Springer, vol. 24(4), pages 895-927, December.
    9. Qian, Zhiguang & Shapiro, Alexander, 2006. "Simulation-based approach to estimation of latent variable models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1243-1259, November.
    10. Helton, J.C. & Johnson, J.D. & Oberkampf, W.L., 2006. "Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links," Reliability Engineering and System Safety, Elsevier, vol. 91(3), pages 320-348.
    11. Khatun, Kaysara & Valdes, Paul J. & Knorr, Wolfgang & Chaturvedi, Rajiv Kumar, 2010. "Assessing the mitigation potential of forestry activities in a changing climate: A case study for Karnataka," Forest Policy and Economics, Elsevier, vol. 12(4), pages 277-286, April.
    12. Berridge, S.J. & Schumacher, J.M., 2004. "Pricing High-Dimensional American Options Using Local Consistency Conditions," Other publications TiSEM 8c8de631-5039-4eec-a965-3, Tilburg University, School of Economics and Management.
    13. Cruz Báez, Domingo Israel & González Rodríguez, José Manuel, 2008. "Valoración de opciones. Un enfoque diferente," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 26, pages 341-362, Abril.
    14. Helton, Jon C. & Pilch, Martin & Sallaberry, Cédric J., 2014. "Probability of loss of assured safety in systems with multiple time-dependent failure modes: Representations with aleatory and epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 171-200.
    15. L'Ecuyer, Pierre, 2004. "Random number generation," Papers 2004,21, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    16. Tsai, Rung-Ching & Bockenholt, Ulf, 2002. "Two-level linear paired comparison models: estimation and identifiability issues," Mathematical Social Sciences, Elsevier, vol. 43(3), pages 429-449, July.
    17. Peter J. Diggle & Irene Kaimi & Rosa Abellana, 2010. "Partial-Likelihood Analysis of Spatio-Temporal Point-Process Data," Biometrics, The International Biometric Society, vol. 66(2), pages 347-354, June.
    18. Djennad, Abdelmajid & Rigby, Robert & Stasinopoulos, Dimitrios & Voudouris, Vlasios & Eilers, Paul, 2015. "Beyond location and dispersion models: The Generalized Structural Time Series Model with Applications," MPRA Paper 62807, University Library of Munich, Germany.
    19. repec:jss:jstsof:08:i13 is not listed on IDEAS
    20. P. Gareth Ridall & Anthony N. Pettitt & Robert D. Henderson & Pamela A. McCombe, 2006. "Motor Unit Number Estimation—A Bayesian Approach," Biometrics, The International Biometric Society, vol. 62(4), pages 1235-1250, December.
    21. Lawrence Joseph, 2007. "Bayesian Core: A Practical Approach to Computational Bayesian Statistics by J. M. MARIN and C. P. ROBERT," Biometrics, The International Biometric Society, vol. 63(3), pages 975-976, September.
    22. A. N. Pettitt & N. Friel & R. Reeves, 2003. "Efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 235-246, February.

    More about this item

    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:taf:quantf:v:12:y:2012:i:10:p:1571-1583. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.