Bergische Universität Wuppertal
Fachbereich Mathematik und Naturwissenschaften
Angewandte Mathematik - Numerische Analysis


Exponential Time Differencing (ETD) Methods for pricing nonlinear Black-Scholes models for path-dependent American options

Masterarbeit Wirtschaftsmathematik

Master's Thesis in Financial Mathematics, Halmstad University, Sweden



In this thesis we consider the work of Yousuf, Khaliq and Kleefeld ...


Exponential Time Differencing, Transaction Cost model, Butterfly Spread, Discrete Barrier Option, Nonlinear Black-Scholes Model, Risk Adjusted Pricing Model


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  2. C. Chiarella, A. Ziogas, Evaluation of American strangles, J. Economic Dynamics & Control 29 (2005), 31-62.
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  4. E. Dremkova, M. Ehrhardt, A high-order compact method for nonlinear Black-Scholes option pricing equations of American options, Int. J. Comput. Math. 88 (2011), 2782-2797.
  5. B. Düring, M. Fournié, A. Jüngel, High order compact finite difference schemes for a nonlinear Black-Scholes equation, Int. J. Theor. Appl. Finance 6 (2003), 767-789.
  6. P.A. Forsyth, K.R. Vetzal, Quadratic convergence of a penalty method for valuing American options, SIAM J. Sci. Comp. 23 (2002), 2096-2123.
  7. P. Heider, Numerical methods for nonlinear Black-Scholes equations, Appl. Math. Finance 17 (2010), 59-81.
  8. H. Imai, N. Ishimura, I. Mottate, M. Nakamura, On the Hoggard-Whalley-Wilmott equation for the pricing of options with transaction costs, Asia Pacific Financial Markets 13 (2006), 315-326.
  9. M. Jandacka, D. Ševčovič, On the risk adjusted pricing methodology based valuation of vanilla options and explanation of the volatility smile, J. Appl. Math. 3 (2005), 235-258.
  10. B. Kleefeld, A.Q.M. Khaliq, B.A. Wade, An ETD Crank-Nicolson Method for Reaction-Diffusion Systems, Numer. Meth. PDE 28 (2012), 1309-1335.
  11. W. Liao, A.Q.M Khaliq, High order compact scheme for solving nonlinear Black-Scholes equation with transaction cost, Int. J. Comput. Math. 86 (2009), 1009-1023.
  12. D. Ševčovič, Transformation methods for evaluating approximations to the optimal exercise boundary for a nonlinear Black-Scholes equation, Canad. Appl. Math. Quarterly 15 (2007), 77-79.
  13. M. Yousuf, A. Khaliq and B. Kleefeld, The numerical approximation of nonlinear Black-Scholes model for exotic path-dependent American options with transaction cost, Int. J. Comput. Math. 89 (2012), 1239-1254.

University of Wuppertal
Faculty of Mathematics and Natural Sciences
Department of Mathematics
Applied Mathematics & Numerical Analysis Group

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