Advertisement

Valuation of European Options with Liquidity Shocks Switching by Fitted Finite Volume Method

  • Miglena N. KolevaEmail author
  • Lubin G. Vulkov
Conference paper
  • 9 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11958)

Abstract

In the present paper, we construct a superconvergent fitted finite volume method (FFVM) for pricing European option with switching liquidity shocks. We investigate some basic properties of the numerical solution and establish superconvergence in maximal discrete norm. An efficient algorithm, governing the degeneracy and exponential non-linearity in the problem, is proposed. Results from various numerical experiments with different European options are provided.

Notes

Acknowledgments

This research is supported by the Bulgarian National Science Fund under Project DN 12/4 from 2017.

References

  1. 1.
    Chernogorova, T., Valkov, R.: Finite volume difference scheme for a degenerate parabolic equation in the zero-coupon bond pricing. Math. Comput. Model. 54, 2659–2671 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Gerisch, A., Griffiths, D.F., Weiner, R., Chaplain, M.A.J.: A Positive splitting method for mixed hyperbolic-parabolic systems. Numer. Meth. Part. Differ. Equat. 17(2), 152–168 (2001)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Gyulov, T.B., Vulkov, L.G.: Well posedness and comparison principle for option pricing with switching liquidity. Nonlinear Anal. Real World Appl. 43, 348–361 (2018)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Hundsdorfer, W., Verwer, J.: Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Springer Series in Computational Mathematics, vol. 33. Springer, Heidelberg (2003).  https://doi.org/10.1007/978-3-662-09017-6CrossRefzbMATHGoogle Scholar
  5. 5.
    Koleva, M.N., Vulkov, L.G.: Fully implicit time-stepping schemes for a parabolic-ODE system of european options with liquidity shocks. In: Lirkov, I., Margenov, S.D., Waśniewski, J. (eds.) LSSC 2015. LNCS, vol. 9374, pp. 360–368. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-26520-9_40CrossRefGoogle Scholar
  6. 6.
    Koleva, M., Mudzimbabwe, W., Vulkov, L.: Fourth-order compact schemes for a parabolic-ordinary system of European option pricing liquidity shocks model. Numer. Algorithms 74(1), 59–75 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ludkovski, M., Shen, Q.: European option pricing with liquidity shocks. Int. J. Theor. Appl. Finance 16(7), 1350043 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Mudzimbabwe, W., Vulkov, L.: IMEX schemes for a parabolic-ODE system of European options with liquidity shocks. J. Comp. Appl. Math. 299, 245–256 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Valkov, R.: Convergence of a finite volume element method for a generalized Black-Scholes equation transformed on finite interval. Numer. Algorithms 68(1), 61–80 (2015)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Wang, S.: A novel fitted finite volume method for the Black-Sholes equation governing option pricing. IMA J. Numer. Anal. 24, 699–720 (2004)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Wang, S., Shang, S., Fang, Z.: A superconvergence fitted finite volume method for Black-Sholes equation governing European and American options. Numer. Meth. Part. Differ. Equ. 31(4), 1190–1208 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of RuseRuseBulgaria

Personalised recommendations