Skip to main content
SpringerLink
Log in

A Numerical Approach to Price Path Dependent Asian Options

  • Conference paper
  • First Online:
Large-Scale Scientific Computing (LSSC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9374))

Included in the following conference series:

  • 702 Accesses

Abstract

In this paper we develop a parabolic-hyperbolic splitting method for resolving the degeneracy of order \(\gamma , \; 0 < \gamma \le 2\) in the ultra-parabolic equation of path dependent Asian options. For the space discretization of the parabolic subproblem we have used two approximations. The first one is the finite volume difference scheme of S. Wang [11], while the second one is the monotone difference scheme of A.A. Samarskii [9]. Some computation results and a comparison between the two methods are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Cen, Z., Le, A., Xu, A.: Finite difference scheme with a moving mesh for pricing Asian options. Appl. Math. Comp. 219(16), 8667–8675 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chernogorova, T.P., Vulkov, L.G.: Two splitting methods for a fixed strike Asian option. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) NAA 2012. LNCS, vol. 8236, pp. 214–221. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  3. Cox, J., Rubinstein, M.: Option Markets. Prentice-Hall, Englewood Cliffs (1985)

    Google Scholar 

  4. Hugger, J.: A fixed strike Asian option and comments on its numerical solution. ANZIAM J. 45(E), C215–C231 (2004)

    MathSciNet  Google Scholar 

  5. Hugger, J.: Wellposedness of the boundary value formulation of a fixed strike Asian option. J. Comp. Appl. Math. 105, 460–481 (2006)

    Article  MathSciNet  Google Scholar 

  6. Marcozzi, M.D.: An addaptive extrapolation discontinuous Galerkin method for the valuation of Asian options. J. Comp. Math. 235, 3632–3645 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  7. Meyer, G.H.: On pricing American and Asian options with PDE methods. Acta Math. Univ. Comenianne LXX 1, 153–165 (2000)

    Google Scholar 

  8. Oosterlee, C.W., Frish, J.C., Gaspar, F.J.: TVD, WENO and blended BDF discretizations for Asian options. Comp. Visual. Sci. 6, 131–138 (2004)

    Article  MATH  Google Scholar 

  9. Samarskii, A.A.: The Theory of Difference Schemes. Marcel Dekker, New York (2001)

    Book  MATH  Google Scholar 

  10. Sengypta, I.: Pricing Asian options in financial markets using Melling transformations. EJDE 2014(234), 1–9 (2014)

    Google Scholar 

  11. Wang, S.: A novel fitted finite volume method for Black-Scholes equation governing option pricing. IMA J. Numer. Anal. 24, 699–720 (2004)

    Article  MathSciNet  Google Scholar 

  12. Wilmott, P., Dewyne, J., Howison, S.: Option Pricing: Mathematical Models and Computation. Oxford Financial Press, Oxford (1993)

    Google Scholar 

  13. Zvan, R., Forsyth, P.A., Vetzal, K.: Robust numerical methods for PDE models of Asian options. J. Comp. Finance 1(2), 39–78 (1998)

    MathSciNet  Google Scholar 

Download references

Acknowledgement

This work was partially supported by the European Union under Grant Agreement number 304 617 (FP7 Marie Curie Action Project Multi-ITN Strike - Novel Methods in Computational Finance) and the Bulgarian Fund of Sciences under Grants No. FNI I 02/9-2014 and No. FNI I 02/20-2014.

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Informatics, University of Sofia, Sofia, Bulgaria

    Tatiana Chernogorova

  2. Faculty of Natural Sciences and Education, University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

Authors
  1. Tatiana Chernogorova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lubin Vulkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tatiana Chernogorova .

Editor information

Editors and Affiliations

  1. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Inst. of Inform. & Communication, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar D. Margenov

  3. Informatics and Mathematical Modell, Technical University of Denmark, Kongens Lyngby, Denmark

    Jerzy Waśniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Chernogorova, T., Vulkov, L. (2015). A Numerical Approach to Price Path Dependent Asian Options. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2015. Lecture Notes in Computer Science(), vol 9374. Springer, Cham. https://doi.org/10.1007/978-3-319-26520-9_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-26520-9_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26519-3

  • Online ISBN: 978-3-319-26520-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation