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High Order Compact Schemes for Option Pricing with Liquidity Shocks

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Part of the book series: Mathematics in Industry ((TECMI,volume 25))

Abstract

This chapter concerns the numerical pricing of European options for markets with liquidity shocks. We derive and analyze high-order weighted compact finite difference schemes (WCFDS). Numerical simulations for the price and Greeks, using WCFDS combined with Richardson extrapolation in time are presented.

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References

  1. Ciment, M., Leventhal, S., Weinberg, B.: The operator compact implicit method for parabolic equations. J. Comput. Phys. 28(2), 135–166 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  2. Dremkova, E., Ehrhardt, M.: A high-order compact method for nonlinear Black-Scholes option pricing equations of American options. Int. J. Comput. Math. 88(13), 2782–2797 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Düring, B. Heuer, C.: High-order compact schemes for parabolic problems with mixed derivatives in multiple space dimensions. SIAM J. Numer. Anal. 53(5), 2113–2134 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Faragó, I., Izsák, F., Szabó, T.: An IMEX scheme combined with Richardson extrapolation methods for some reaction-diffusion equations. Quart. J. Hung. Meteor. Serv. 117(2), 201–218 (2013)

    Google Scholar 

  5. Koleva, M.N., Mudzimbabwe, W., Vulkov, L.G.: Fourth-order compact schemes for a parabolic-ordinary system of European option pricing liquidity shocks model. Numer. Algorithms 74(1), 59–75 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kreiss, H.O., Thomee, V., Widlund, O.: Smoothing of initial data and rates of convergence for parabolic difference equations. Commun. Pure Appl. Math. 23, 241–259 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  7. Liao, W., Khaliq, A.Q.M.: High order compact scheme for solving nonlinear Black-Scholes equation with transaction cost. Int. J. Comput. Math. 86(6), 1009–1023 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ludkovski, M., Shen, Q.: European option pricing with liquidity shocks. Int. J. Theory Appl. Financ. 16(7), 1350043 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Mudzimbabwe, W., Vulkov, L.G.: IMEX schemes for a parabolic-ODE system of European options with liquidity shock. J. Comput. Appl. Math. 299, 245–256 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. Tangman, D.Y., Gopaul, A., Bhuruth, M.: Numerical pricing of options using high-order compact finite difference schemes. J. Comput. Appl. Math. 218, 270–280 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang, L., Chen, W., Wang, C.: An energy-conserving second order numerical scheme for nonlinear hyperbolic equation with exponential nonlinear term. J. Comput. Appl. Math. 280, 347–366 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This research was supported by the European Union under Grant Agreement number 304617 (FP7 Marie Curie Action Project Multi-ITN STRIKE—Novel Methods in Computational Finance) and the Bulgarian National Fund of Science under Project I02/20-2014.

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Correspondence to Miglena N. Koleva .

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Koleva, M.N., Mudzimbabwe, W., Vulkov, L.G. (2017). High Order Compact Schemes for Option Pricing with Liquidity Shocks. In: Ehrhardt, M., Günther, M., ter Maten, E. (eds) Novel Methods in Computational Finance. Mathematics in Industry(), vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-61282-9_18

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