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

People Research Publications Teaching

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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

Supervision

• Prof. Dr. Matthias Ehrhardt

Description

Keywords

References:

1. J. Ankudinova, M. Ehrhardt, Fixed Domain Transformations and Split-Step Finite Difference Schemes for Nonlinear Black-Scholes Equations for American Options, Chapter 8 in M. Ehrhardt (ed.) Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing, Nova Science Publishers, Inc., Hauppauge, NY 11788, (2008), pp. 243-273.
2. C. Chiarella, A. Ziogas, Evaluation of American strangles, J. Economic Dynamics & Control 29 (2005), 31-62.
3. S.M. Cox, P.C. Matthews, Exponential Time Differencing for Stiff Systems, J. Comput. Phys. 176 (2002), 430-455.
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.