Abstract
A finite element method and a simple lattice method are proposed for numerical valuation of American options under a regime switching model. Their stability estimates are established. Numerical results are presented to compare our methods and to examine their accuracy for various combinations of parameters. The dependency of early exercise prices and option prices on parameters are also investigated numerically.
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References
Adams, R.A.: Sobolev Spaces. Academic Press, New York (1975)
Allegretto, W., Lin, Y., Yang, H.: Finite element error estimates for a nonlocal problem in American option valuation. SIAM J. Numer. Anal. 39, 834–857 (2001)
Baiocchi, C., Capelo, A.: Variational and Quasivariational Inequalities. Wiley, New York (1984)
Barone-Adesi, G., Whaley, R.E.: Efficient analytic approximation of American option values. J. Finance 42, 301–320 (1987)
Badea, L., Wang, J.: A new formulation for the valuation of American options, I: Solution uniqueness & II: Solution existence. In: Park, E.-J., Lee, J. (eds.) Analysis and Scientific Computing, Proceeding of the 19th Daewoo Workshop in Analysis and Scientific Computing, pp. 3–33 (2000)
Buffington, J., Elliott, R.J.: American options with regime switching. Int. J. Theor. Appl. Finance 5, 497–514 (2002)
Carr, P., Chesney, M.: American Put Call Symmetry. Working paper, November 13 (1996). (http://www.math.nyu.edu/research/carrp/research.html)
Cont, R., Tankov, P.: Financial Modelling with Jump Processes. Chapman & Hall/CRC, Boca Raton (2004)
Fajardo, J., Mordecki, E.: Symmetry and duality in Levy markets. Quant. Finance 6, 219–227 (2006)
Fouque, J.-P., Papanicolaou, G., Sircar, K.R.: Derivatives in Financial Markets with Stochastic Volatility. Cambridge University Press, Cambridge (2000)
French, D.A., King, J.T.: Analysis of a robust finite element approximation for a parabolic equation with rough boundary data. Math. Comput. 60, 79–104 (1993)
Glowinski, R., Lions, J.L., Trémolières, R.: Numerical Analysis of Variational Inequalities. North-Holland, Amsterdam (1981)
Guo, X., Zhang, Q.: Closed-from solutions for perpetual American put options with regime switching. SIAM J. Appl. Math. 64, 2034–2049 (2004)
Holmes, A.D., Yang, H.: A front-fixing finite element method for the valuation of American options. SIAM J. Sci. Comput. 30, 2158–2180 (2008)
Peskir, G., Shiryaev, A.N.: A note on the call-put parity and a call-put duality. Theory Probab. Appl. 46, 181–183 (2001)
Zhu, Y.-L., Wu, X., Chern, I.-L.: Derivative Securities and Difference Methods. Springer, Berlin (2004)
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This research was supported in part by NSF grant DMS–0749676.
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Yang, H. A Numerical Analysis of American Options with Regime Switching. J Sci Comput 44, 69–91 (2010). https://doi.org/10.1007/s10915-010-9365-2
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DOI: https://doi.org/10.1007/s10915-010-9365-2